Question

Determine the value of log 18 base 12+log 8 base 12

Answer 1

the answer is in the attachment.

Answer 2

Answer:

Value of given Expression is 2

Step-by-step explanation:

Given Expression is $log_{12}\,18+log_{12}\,8$

To find: Value of given Expression

Consider,

$log_{12}\,18+log_{12}\,8$

use law of logarithmic function, $log_a\,b=\frac{log\,b}{log\,a}$

we get,

$\implies \frac{log\,18}{log\,12}+\frac{log\,8}{log\,12}$

$\implies \frac{log\,18+log\,8}{log\,12}$

use another law of logarithmic function, $log\,ab=log\,a+log\,b$

we get,

$\implies \frac{log\,(18\times8)}{log\,12}$

$\implies \frac{log\,144}{log\,12}$

$\implies \frac{log\,12^2}{log\,12}$

we have to use another law of logarithmic function, $log\,a^b=b\:log\,a$

we get,

$\implies \frac{2\:log\,12}{log\,12}$

$\implies2$

Therefore, Value of given Expression is 2