Question

How do you solve `3 log_5 x - log_5 4 = log_5 16`?

Answer 1

The answer is `x=4`

Explanation:

To solve this equation you have to use the facts that:

1. `a*log_b(c)=log_b(c^a)`
2. `log_a(b)-log_a(c)=log_a (b/c)`

First you use (1) to get:

`log_5(x^3) -log_5(4)=log_5(16)`

Then you use (2) to get:

`log_5(x^3/4) =log_5(16)`

Now you can leave the logarithms (they both have the same base)

`x^3/4=16`

`x^3=64`

`x=4` (because `4^3=4*4*4=64`)