Question

Rewrite the logarithm as a ratio of common logarithms and natural logarithms. log4 45

Answer 1

Answer:

Common logarithm

$log_451= \frac{log_1_045}{log_1_08}$

Natural logarithms

$log_445= \frac{log_e45}{log_e4}$

or

$log_445= \frac{In45}{In4}$

Step-by-step explanation:

From the question we are told that

$Log_445$

Generally converting log from base x to base 10 si mathematically represented as

$log_xa=log_1_0a *log_x10$

$log_xa= \frac{log_1_0a}{log_1_0x}$

Therefore

Common logarithm

$log_451= \frac{log_1_045}{log_1_08}$

Generally Natural logarithms $log_ex\ or\ inx$ is mathematically represented as

$log_xa= \frac{log_ea}{log_ex}$

Therefore

Natural logarithms

$log_445= \frac{log_e45}{log_e4}$

or

$log_445= \frac{In45}{In4}$