Question

Find the exact solution using common logarithms 2^5x+3= 3^2x+1

Answer 1

`2^(5x + 3) = 3^(2x + 1)`

`log_(2)(2^(5x + 3)) = log_(2)(3^(2x + 1))`

`(5x + 3)log_(2)(2) = (2x + 1)log_(2)(3)`

`5x + 3 = 1.58(2x + 1)`

`5x + 3 = 3.16x + 1.58`

`1.84x + 3 = 1.58`

`1.84x = -1.42`

`x \approx -0.77`