# Calculator Techniques for ENGINEERING BOARD EXAM: Solving for X, USING SHIFT SOLVE | 10 PROBLEMS

TLDRThis video tutorial focuses on calculator techniques for solving equations in the context of an engineering board exam. It covers basic solving for x, using shift solve for accuracy, and handling simultaneous equations. The instructor emphasizes the importance of providing an initial value of x close to the possible answer to ensure correct results. The video includes ten problems with solutions, demonstrating the use of calculator functions like alpha and shift solve, and highlights common mistakes to avoid.

### Takeaways

- ๐ The video focuses on calculator techniques for solving equations in the context of an engineering board exam.
- ๐ Importance is placed on using the 'shift solve' function properly to ensure accurate results when solving for 'x'.
- ๐ Students are often cautioned about using incorrect initial values in 'shift solve' which can lead to inaccurate answers.
- โ The presenter demonstrates how to correctly input equations into the calculator, including handling exponents and parentheses.
- ๐ข Examples are provided to illustrate the process of using the calculator to solve various mathematical problems, including exponential and logarithmic equations.
- ๐ The video emphasizes the need for selecting an initial value for 'x' that is close to the expected answer to improve the accuracy of the 'shift solve' function.
- ๐ The presenter explains the potential issue of finding only one root when using 'shift solve' on quadratic equations, as opposed to the two roots that may exist.
- ๐ The video script includes a step-by-step guide on how to use the calculator for different types of problems, including checking answers by recalculating equation sides.
- ๐ The script covers how to approach problems involving powers and roots, and how to verify answers by substituting back into the original equation.
- ๐ The final takeaway is an encouragement for viewers to practice calculator skills, as these techniques are applicable in various mathematical areas, including those that may appear in an engineering board exam.
- ๐ The video concludes with an invitation for viewers to subscribe to the channel for more calculator technique tutorials, particularly useful for those preparing for board exams.

### Q & A

### What is the main topic discussed in the video?

-The main topic discussed in the video is calculator techniques for solving equations and problems, specifically for the engineering board exam.

### Why is it important to provide an initial value of x when using the shift solve function on a calculator?

-It is important to provide an initial value of x when using the shift solve function because the calculator uses this value to start the calculation. If the initial value is far from the correct answer, the calculator might provide an inaccurate result.

### What is the correct initial value of x to use when solving the equation 9^x = 5 using the shift solve technique?

-The correct initial value of x to use is not explicitly stated, but the video suggests using a value close to the choices provided in a multiple-choice question, such as 0.7 or 0.732, to ensure accuracy.

### How does the video demonstrate solving the equation 4^(2x + 1) = 1024?

-The video demonstrates solving the equation by using the shift solve technique on a calculator, inputting the equation, and then providing an initial value for x to find the solution.

### What is the final answer for the equation 4^(2x + 1) = 1024 in the video?

-The final answer for the equation 4^(2x + 1) = 1024 is 16, which is 4 raised to the power of the found value of x.

### Why is it recommended to use shift solve instead of the colon method for certain problems in the video?

-It is recommended to use shift solve instead of the colon method for certain problems because shift solve can provide more accurate results, especially when dealing with equations that have multiple roots or involve small discrepancies.

### What is the significance of using the correct base when solving logarithmic equations in the video?

-The significance of using the correct base when solving logarithmic equations is to ensure the accuracy of the solution, as the base can change the value of the logarithm and thus the result of the equation.

### How does the video handle the problem of finding the value of 3 raised to the power of 4x given that 9^x = 5?

-The video first finds the value of x using the shift solve technique, and then substitutes this value into the expression 3^(4x) to evaluate the final result.

### What is the advice given in the video for solving equations that involve exponents and logarithms with different bases?

-The advice given in the video is to ensure that the calculator is set to the correct base when performing logarithmic operations and to use the shift solve technique for finding the values of variables in the equations.

### What is the final problem discussed in the video and what is the solution?

-The final problem discussed in the video involves solving for 'a' in the equation log2(a+2) + log2(a-2) = 5. The solution provided is a = 6.

### Outlines

### ๐งฎ Introduction to Calculator Techniques for Solving Equations

This paragraph introduces the topic of using calculator techniques for solving equations in the context of engineering board exams. It emphasizes the importance of using the correct calculator functions, particularly when solving for 'x' in basic equations and simultaneous equations. The speaker highlights the common mistake of using incorrect initial values for 'x', which can lead to inaccurate results. The video aims to teach viewers how to properly use the 'shift solve' function to ensure accurate solutions.

### ๐ Demonstrating Shift Solve Technique with an Example

The speaker provides a step-by-step demonstration of using the 'shift solve' technique to solve an equation involving exponents. The example given is 9 raised to the power of 6 equals 3 raised to the power of 2x. The process involves writing the equation on the calculator, using the 'shift solve' function, and choosing an initial value for 'x' that is close to the expected solution. The speaker shows how different initial values can be tested to confirm the correct answer, which in this case is 8.5.

### ๐ Applying Calculator Techniques to Linear Equations

This paragraph discusses the application of calculator techniques to solve a linear equation: 7x - 5(x + 1) = 2(3 - x) - 5. The speaker explains the importance of correctly handling the signs and parentheses when inputting the equation into the calculator. The 'shift solve' method is used again, and the speaker demonstrates how to input an initial value for 'x' and how to verify the solution by comparing both sides of the equation.

### ๐ข Solving Logarithmic Equations Using Calculator Techniques

The focus shifts to solving logarithmic equations, starting with an example where the equation involves logarithms with base 10. The speaker explains the process of inputting the equation into the calculator, using the 'log' function, and applying the 'shift solve' technique. The example provided is solving for 'x' in the equation log(x^2) - log(5x) = log(20), and the correct value of 'x' that satisfies the equation is found to be 100.

### ๐ Calculating Exponential Expressions with Given Powers

The paragraph discusses how to find the value of an exponential expression given a power, as in the equation 4^(2x + 1) = 1024. The speaker demonstrates using the calculator to solve for 'x' first and then calculating the value of 4^x using the found value. The distinction is made that the problem asks for 4^x, not just 'x', and the correct answer is 16, which is 4 raised to the power of the found value of 'x', which is 2.

### ๐ Evaluating Powers of Three Using Calculator Techniques

This paragraph presents a problem involving powers of three and five, where the equation 9^x = 5 leads to finding the value of 3^(4x). The speaker uses the 'shift solve' function to find the value of 'x' and then substitutes it into the expression 3^(4x) to find the final answer. The process is demonstrated with different initial values to ensure the accuracy of the solution, which is confirmed to be 25.

### ๐ Solving Equations with Negative Exponents

The speaker tackles an equation with negative exponents, 16^(-x + 1) = 8, and uses the 'shift solve' function to find the value of 'x'. The process is shown with different initial values to verify the solution, which is consistently found to be 0.25 or one-fourth. The speaker emphasizes the ease of solving such problems with calculator techniques.

### ๐ Dealing with Equations Involving Multiple Exponents

The paragraph covers solving an equation with multiple instances of exponents, 3^x * 5^(x + 1) = 6^(x + 2). The speaker advises using the 'shift solve' function due to the sensitivity of the calculator with decimal values and demonstrates finding the correct value of 'x' by inputting different initial values. The correct answer is found to be approximately 2.1544, corresponding to choice 'd'.

### ๐ Solving Logarithmic Equations with Different Bases

The focus is on solving logarithmic equations where the base is not 10, starting with an example where the base is 4. The speaker explains how to input the base into the calculator and demonstrates solving for 'x' in the equation 2log_x - log_4(9) = 2. The process involves using the 'shift solve' function with an initial value for 'x', and the correct solution is found to be 12.

### ๐ Final Problem Involving Logarithms with Base 3

The final problem involves a logarithmic equation with base 3, log_3(81^x) = 16. The speaker shows how to input the equation into the calculator, using the 'log' function with the specified base, and applies the 'shift solve' technique. The correct value of 'x' is consistently found to be 4, regardless of the initial value inputted.

### ๐ Conclusion and Invitation to Learn More Calculator Techniques

The speaker concludes the video by summarizing the importance of mastering calculator techniques for solving various mathematical problems, especially for those preparing for board exams. An invitation is extended to subscribe to the channel for more content on calculator techniques, covering a range of mathematical topics from algebra to advanced engineering mathematics. The speaker expresses gratitude for the viewers' attention and offers well-wishes for their success in exams.

### Mindmap

### Keywords

### ๐กCalculator Techniques

### ๐กEngineering Board Exam

### ๐กSolving for X

### ๐กShift Solve

### ๐กAlgebra

### ๐กInitial Value

### ๐กMultiple Choice

### ๐กExponential Functions

### ๐กLogarithmic Functions

### ๐กEquation

### Highlights

Introduction to calculator techniques for solving equations in the engineering board exam.

The importance of using the correct initial value of x when using shift solve to avoid inaccurate results.

How to properly use shift solve for basic equations to find the value of x accurately.

The process of solving the first problem involving powers of 3 and 9 to find the value of x.

Using calculator functions to write and solve equations, including the use of alpha and calc keys.

The method of verifying the calculator's answer by substituting the value of x back into the equation.

Solving a linear equation using shift solve and the significance of parentheses in calculator input.

The potential for a calculator to provide only one root when solving quadratic equations with shift solve.

How to approach logarithmic equations using calculator techniques and base considerations.

Solving an equation involving logarithms with base 4 to find the value of x.

The technique of using shift solve to find the value of 4 raised to the power of x, not just x.

The process of solving an equation with an exponent to find the value of three raised to four times x.

Using shift solve with caution when dealing with equations involving decimals and small discrepancies.

The method of solving for x in an equation involving the multiplication of powers with different bases.

How to solve logarithmic equations with different bases using the calculator's log function.

The final problem's solution technique involving the sum of logarithms with base 2 to find the value of a.

Conclusion and encouragement for subscribers to learn more calculator techniques for the engineering board exam.

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