Question

What is the equation below solved for x to the nearest hundredth?

`log_5(x+2)+log_5 7=1`

Answer 1

`x=-9/7`

Explanation:

This is what I did to solve it:

You can multiply the `x+2` and the `7` and it will turn into:

`log_5(7x+14)`

Then the `1` can be turned into:

`log_"5"5`

The current state of the equation is:

`log_5(7x+14) = log_"5"5`

You can then cancel the "logs" out and it will leave you with:

`color(red)cancel(color(black)log_color(black)5)(7x+14)=color(red)cancel(color(black)log_color(black)"5")5`

`7x+14 = 5`

From here you just solve for x:

`7x color(red)cancel(color(black)(-14))=5-14`

`7x=-9`

`color(red)cancel(color(black)(7))x=-9/7`

If somebody could double check my answer that would be great!