Question

How do you solve `5 - 3^x = - 40`?

Answer 1

`x = 2+log_3(5)~~3.465`

Explanation:

`5-3^x = -40`

Subtract `5` from each side of the equation.

`-3^x = -45`

Multiply both sides of the equation by `-1`.

`3^x = 45`

Take the base-`3` logarithm of each side of the equation.

`log_3(3^x) = log_3(45)`

Apply the rule `log_a(a^x) = x` to the left hand side.

`x = log_3(45)`

Apply the rule `log(ab) = log(a)+log(b)` to the right hand side.

`x = log_3(9*5) = log_3(9)+log_3(5)`

Apply the rule `log_a(a^x) = x` to `log_3(9)=log_3(3^2)`

`x = 2+log_3(5)~~3.465`