Question

Can anyone help me solve a logarithm question?​

Answer 1

Answer:

$x=1$

Step-by-step explanation:

Given equation in the question is,

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

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

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

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

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

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

$2=5x-3$

$2+3=5x$

$5x=5$

$x=1$