Can anyone help me solve a logarithm question?

asked Oct 23, 2022 85.0k views

1 vote

5.2k points

Please log in or register to add a comment.

4 votes

Answer:

x=1

Explanation:

Given equation in the question is,

$\frac{2}{\text{log}_x(xy)}+\frac{2}{\text{log}_x(xy)}+3=5x$ '

Since,
$\text{log}_a}(xy)=\frac{\text{log(a)}}{\text{log}(xy)}$

$\frac{2\text{log}x}{\text{log}(xy)}+\frac{2\text{log}y}{\text{log}(xy)}+3=5x$

$\frac{2(\text{log}x)+2(\text{log}y)}{\text{log}(xy)}=5x-3$

$\frac{2[\text{log}(x)+\text{log}(y)]}{\text{log}(xy)}=5x-3$

$\frac{2\text{log}(xy)}{\text{log}(xy)}=5x-3$

2=5x-3

2+3=5x

5x=5

x=1

Katsu answered Oct 28, 2022

by Katsu

5.7k points

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

5.6m questions

7.3m answers