Question

How do you solve `\log _ { 4} x + \log _ { 4} ( x + 8) = 2`?

Answer 1

`x=1.65`

Explanation:

First let's turn 2 into a log with a base of 4
`log_4 16=2`

On the RHS when two logs of the same base are added, they are multiplied by each other. This makes the problem look like this:

`log_4 (x^2+8x) = log_4 16`

We can now get rid of the logs to give this equation:
`x^2+8x=16`
`x^2+8x-16=0`

Now use the quadratic formula to get the values of `x` since the equation is in the form of `ax^2+bx+c=0`.

`x= 1.65`