Question

evaluate the expression without using a calculator.
log 10
log 10 = \square

Explanation:

Step1: Recall log base 10 definition

The logarithm \(\log x\) (without a specified base) is base - 10, so \(\log_{10}x\). By the definition of a logarithm, if \(y = \log_{b}x\), then \(x=b^{y}\). For \(\log_{10}10\), we want to find \(y\) such that \(10^{y}=10\).

Step2: Solve for y

We know that for the exponential function \(f(y)=10^{y}\), when \(y = 1\), \(10^{1}=10\). So, if \(10^{y}=10\), then \(y = 1\). Therefore, \(\log_{10}10=1\).

Answer:

\(1\)