Find the value of x: (3^x)(5^(x+1))=6^(x+2)

Question

If you can explain it will be a big help thankss

Answer 1

We take the logs of both sides.

x ln 3 + (x+1)ln 5 = (x+2) ln 6

Then, x(ln 3 + ln 5 - ln 6) = 2 ln 6 - ln 5

x = (2 ln 6 -ln 5)/ln3+ln 5 - ln 6)

Then, x = 2.154426

Alternatively, we could have written

x = ln(36/5)/ln(5/2)