Question

How do you solve `9^ { 8x + 7} = 6^ { 5- 4x }`?

Answer 1

I got: `x=-0.25952`

Explanation:

We can try applying the natural log on both sides:
`ln(9)^(8x+7)=ln(6)^(5-4x)`
use a property of logs:
`(8x+7)ln(9)=(5-4x)ln(6)`
rearrange:
`8xln(9)+7ln(9)=5ln(6)-4xln(6)`
collect:
`8xln(9)+4xln(6)=5ln(6)-7ln(9)`
`x[8ln(9)+4ln(6)]=5ln(6)-7ln(9)`
so that:
`x=[5ln(6)-7ln(9)]/[8ln(9)+4ln(6)]=-0.25952`