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

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.

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.

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.

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.

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.

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.

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.

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'.

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.

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.

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.