Question

How do you solve this logarithmic equation? `3log_(5)x-log_(5)(5x)=3-log_(5)25`

Answer 1

`{5}`

Explanation:

Put all logarithms to one side:

`3log_5 x - log_5 (5x) + log_5 25 = 3`

`log_5 25` can be rewritten as `(log25)/(log5) = (2log5)/(log5) = 2`

`log_5 x^3 - log_5 (5x) + 2 = 3`

`log_5 x^3 - log_5 5x = 1`

`log_5((x^3)/(5x)) = 1`

`x^2/5 = 5^1`

`x^2 = 25`

`x = +- 5`

The `-5` solution is extraneous, since `log_5(ax)`, where `a` is a positive constant is only defined in the positive-x-values.

Hopefully this helps!