Question

How do you solve for x in `2^x = 5^(x+6)`?

Answer 1

Taking the logarithm on both sides we get
`xln(2)=(x+6)ln(5)`
rearranging we obtain
`x(ln(2)-ln(5))=6ln(5)`
so
`x=(6ln(5))/(ln(2)-ln(5))`

Explanation:

We used that `ln(x^r)=rln(x)`