Question

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

Answer 1

0.4077

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