Question

How do you solve `log_5(x) + log_3(x) =1`?

Answer 1

I found: `x=1.921148`

Explanation:

We can change base:
`(ln(x))/(ln(5))+(ln(x))/(ln(3))=1`
`ln(x)(1/ln(5)+1/(ln(3)))=1`
`ln(x)[1.531574]=1`
`ln(x)=1/1.531574=0.652923`

use the definition of log:

`x=e^0.652923=1.921148`