Question

find the value of p in
$(\frac{3}{5})^{p} ( \frac{5}{3}) ^{2p} = \frac{125}{27}$
​

Answer 1

p = 3

Step-by-step explanation:

Given:

$(\dfrac{3}{5})^{p} \times ( \dfrac{5}{3}) ^{2p} = \frac{125}{27}$

To find:

The value of p

Solution:

We have to do nothing just we have to make equal base from both side. As its easy to eliminate. Then, using some laws of Indices we will get the answer.

$(\frac{3}{5})^{p} \times ( \frac{5}{3}) ^{2p} = \frac{125}{27} \\ \\ {( \frac{5}{3}) }^{ - p} \times {( \frac{5}{3}) }^{ 2p} = {( \frac{5}{3}) }^{3} \: \: \: \: [\text{Using 1}] \\ \\ {( \frac{5}{3} )}^{(2p - p)} ={( \frac{5}{3}) }^{3} \: \: \: \: [\text{Using 2}] \\ \\ {( \frac{5}{3}) }^{p} = {( \frac{5}{3}) }^{3} \\ \\ [\text{Eliminiting the base from both sides}] \\ \\ p = 3$

The required value of p is 3 .

Basic laws of