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The equation provided is:

\[
7 \times (3^x) + 3^2 + 3^2 = 9^x \times 27 \times (3^x) \times 9(3^x)
\]

Let's solve for \( x \).

### Step 1: Simplify both sides of the equation.

#### Left side:
\[
7 \times 3^x + 9 + 9 = 7 \times 3^x + 18
\]

#### Right side:
Notice that \( 9^x = (3^2)^x = 3^{2x} \) and \( 9(3^x) = 9 \times 3^x = 3^2 \times 3^x = 3^{x+2} \).

So the right side becomes:
\[
3^{2x} \times 27 \times 3^x \times 3^{x+2}
\]
Now, let's rewrite \( 27 \) as \( 3^3 \):
\[
3^{2x} \times 3^3 \times 3^x \times 3^{x+2}
\]
Combine all the powers of \( 3 \):
\[
3^{2x+3+x+x+2} = 3^{4x+5}
\]

### Step 2: Set the simplified left side equal to the simplified right side:
\[
7 \times 3^x + 18 = 3^{4x+5}
\]

### Step 3: Compare the powers of \( 3 \):
This is not easily factorable or directly comparable because of the mixed terms. Solving this equation typically requires numerical methods or approximation techniques, as it is transcendental.

Given this complexity, and since this is not easily factorizable in the typical algebraic sense, the exact value of \( x \) likely needs to be found using numerical methods or by estimating.

Would you like to go further with an approximate solution, or do you have additional information?

Explore the solution to the exponential equation 7 * (3^x) + 18 = 3^(4x+5) with detailed step-by-step calculations. This problem involves advanced algebraic concepts such as exponential laws and transcendental equations. Suitable for advanced high school and college-level students.

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