Question

How do you solve `5^(2x-1) = 7^(2x)`?

Answer 1

`x = frac{log 5}{2(log 5 - log 7)}`

Explanation:

`log 5^{2x - 1} = log 7^{2x}`

`(2x - 1) log 5 = 2x log 7`

`x (2 log 5 - 2 log 7) = 1 log 5`

`x = frac{log 5}{log 25 - log 49}`

`(25/49)^x = 5`