Question

Which is the solution to 5^x=8^x-7

Answer 1

x = 30.97 ( to nearest hundredth).

Explanation:

5^x = 8^x-7

Taking logs of both sides:-

ln 5^x = ln 8^x

By the law of logarithms:-

x ln 5 = (x - 7) ln 8

x / (x - 7) = ln 8 / ln 5

x / (x - 7) = 1.292

x = 1.292x - 9.044

1.292x - x = 9.044

x = 9.044 / 0.292

= 30.97 (answer)