Question

The value of log 27/8 base 2/3??

Answer 1

Step-by-step explanation:

answer is in the above picture

Answer 2

$\log_{\frac{2}{3}} (\frac{27}{8})=-3$

Step-by-step explanation:

Given : Expression  log $\frac{27}{8}$ base $\frac{2}{3}$ .

To find : The value of expression ?

Solution :

The expression is written as,  $\log_{\frac{2}{3}} (\frac{27}{8})$

Solving the expression,

$\log_{\frac{2}{3}} (\frac{27}{8})=\log_{\frac{2}{3}} (\frac{3^3}{2^3})$

$\log_{\frac{2}{3}} (\frac{27}{8})=\log_{\frac{2}{3}} (\frac{3}{2})^3$

$\log_{\frac{2}{3}} (\frac{27}{8})=\log_{\frac{2}{3}} (\frac{2}{3})^{-3}$

Applying logarithmic property, $\log a^x=x\log a$

$\log_{\frac{2}{3}} (\frac{27}{8})=-3\log_{\frac{2}{3}} (\frac{2}{3})$

We know, $\log_a a=1$

$\log_{\frac{2}{3}} (\frac{27}{8})=-3(1)$

$\log_{\frac{2}{3}} (\frac{27}{8})=-3$

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