Question

How do you solve `2log_5x = log_5 9`?

Answer 1

First simplify using the rule `alogn = logn^a`

Explanation:

`log_5(x^2) = log_5(9)`

Put everything to one side of the equation.

`0 = log_5(9) - log_5(x^2)`

Simplify using the rule `log_am - log_an = log_a(m / n)`

`0 = log_5(9/x^2)`

Convert to exponential form.

`5^0 = 9/x^2`

`1 = 9/x^2`

`x^2 = 9`

`x = +-3`

However, only +3 works as a solution because the log of a negative number is non-defined.

The solution set is x = 3.

Hopefully this helps!