The problem asks us to find the value of $f(10^{-5})$ given that $f(x) = \log(x)$.

AlgebraLogarithmsFunction EvaluationExponents
2025/5/2

1. Problem Description

The problem asks us to find the value of f(105)f(10^{-5}) given that f(x)=log(x)f(x) = \log(x).

2. Solution Steps

We are given the function f(x)=log(x)f(x) = \log(x). We want to find f(105)f(10^{-5}).
We substitute x=105x = 10^{-5} into the function:
f(105)=log(105)f(10^{-5}) = \log(10^{-5}).
Recall that logb(bx)=x\log_{b}(b^x) = x. Since the logarithm without a specified base is base 10, we have log10(105)=5\log_{10}(10^{-5}) = -5.

3. Final Answer

The final answer is -5.

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