Solve the Inverse Logarithm: Finding (log₇x)⁻¹

$(\log_7x)^{-1}=$

To solve this problem, we must determine the reciprocal of the logarithm expression $\log_7 x$. This involves finding the inverse using the properties of logarithms.

• Step 1: Recognize that the expression $(\log_7 x)^{-1}$ is asking for the reciprocal of the logarithm.
• Step 2: Apply the inverse property of logarithms: $(\log_b a)^{-1} = \log_a b$.

Applying this property to our problem, we set $b = 7$ and $a = x$. Therefore, $(\log_7 x)^{-1}$ transforms to:

$\log_x 7$

Thus, the value of the expression $(\log_7 x)^{-1}$ is $\log_x 7$.

Therefore, the solution to the problem is $\log_x 7$.