Question

evaluate the following logarithmic expression without the use of a calculator. write your answer as a fraction reduced to lowest terms.
log(10)

Explanation:

Step1: Recall logarithm definition

The common logarithm $\log(x)$ is base - 10, so $\log(10)$ means $\log_{10}(10)$. By the definition of a logarithm, if $y = \log_{b}(x)$, then $x=b^{y}$. For $y = \log_{10}(10)$, we want to find $y$ such that $10^{y}=10$.

Step2: Solve for y

We know that for any non - zero number $a$, $a^{1}=a$. So when $a = 10$, $10^{1}=10$. Comparing with $10^{y}=10$, we can see that $y = 1$.

Answer:

1