Question

7 rewrite the following logs with base 10:
$log_{26} 18 = square$
$log_{99} 32 = square$
$log_{12} 4 = square$

Explanation:

Step1: Apply change of base formula

The change of base formula for logarithms is $\log_b a = \frac{\log_{10} a}{\log_{10} b}$, where $\log_{10}$ is the common logarithm (base 10).

Step2: Rewrite first logarithm

For $\log_{26} 18$, substitute $a=18$, $b=26$ into the formula:
$\log_{26} 18 = \frac{\log_{10} 18}{\log_{10} 26}$

Step3: Rewrite second logarithm

For $\log_{99} 32$, substitute $a=32$, $b=99$ into the formula:
$\log_{99} 32 = \frac{\log_{10} 32}{\log_{10} 99}$

Step4: Rewrite third logarithm

For $\log_{12} 4$, substitute $a=4$, $b=12$ into the formula:
$\log_{12} 4 = \frac{\log_{10} 4}{\log_{10} 12}$

Answer:

$\log_{26} 18 = \frac{\log_{10} 18}{\log_{10} 26}$
$\log_{99} 32 = \frac{\log_{10} 32}{\log_{10} 99}$
$\log_{12} 4 = \frac{\log_{10} 4}{\log_{10} 12}$