What is the solution of the equation 9^2x=6? Round your answer to the nearest ten-thousandth.

0.3522

2.4526

0.4077

1.4851

0.4077

Step-by-step explanation:

It's important to use parenthesis to avoid confusion.

9^ (2x) = 6

Use exponent properties:

(9^2) ^x = 6

81^x = 6

Take log of both sides

ln (81^x) = ln (6)

Use log properties:

x ln (81) = ln (6)

Solve for x:

x = ln (6) / ln (81)

x ≈ 0.4077