Question

Can anyone help me solve a logarithm question?​

Answer 1

`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`