Explore: Change of Base Rule Solutions

Change of Base Rule Solutions

Change of Base Rule

The variables a, b, and X are positive real numbers, and $a \neq 1, b \neq 1$ .

Log of any base:

\log_{b} X = \frac{\log_{a} X}{\log_{a} b}

Common log:

\log_{b} X = \frac{\log X}{\log b}

The Change of Base Rule is used to rewrite logarithms , so they have the same base. 
Use the rule when you: 
- have an expression or equation with multiple bases. 
- need a common base to approximate logs with technology.

Write the expression with common logs using the Change of Base Rule.

$\frac{\log {(8)}^{3}}{\log m} = \frac{3 \log 8}{\log m}$

Explain 

$\frac{\log 2 x}{\log 6} + \frac{\log 3}{\log 5} = \frac{\log 2 + \log x}{\log 6} + \frac{\log 3}{\log 5}$

Explain 