log9 (3log2 (1 + log3 (1 + 2log2x))) = 1/2. Find x.Choices:- None of the above 1 12/30 2

To solve the equation, we need to follow these steps:

1. We know that log base a of a equals 1. So, we can rewrite the equation as: 3log2 (1 + log3 (1 + 2log2x)) = 9^(1/2) = 3.

2. Divide both sides by 3 to isolate the inner expression: log2 (1 + log3 (1 + 2log2x)) = 1.

3. Use the property of logarithms that says log base a of a equals 1 to rewrite the equation as: 1 + log3 (1 + 2log2x) = 2^1 = 2.

4. Subtract 1 from both sides to isolate the inner expression: log3 (1 + 2log2x) = 2 - 1 = 1.

5. Use the property of logarithms that says log base a of a equals 1 to rewrite the equation as: 1 + 2log2x = 3^1 = 3.

6. Subtract 1 from both sides to isolate the inner expression: 2log2x = 3 - 1 = 2.

7. Divide both sides by 2 to isolate the inner expression: log2x = 2 / 2 = 1.

8. Use the property of logarithms that says log base a of a equals 1 to rewrite the equation as: x = 2^1 = 2.

So, the solution to the equation is x = 2.