Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth....

Question

5^x-3=3^2x

 

Answer 1

5^x - 3 = 3^2x can be shown to have no real solutions.

 

I assume therefore that you meant 5^x-3 = 3^2x

 

Take logs of both sides:

 

x - 3 = log₅ 3^2x

 

x - 3 = 2x log₅ 3

 

(1 - 2 log₅ 3)x = 3

 

x = 3/(1 - 2 log₅ 3) ≈ -8.214