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

Question

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

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Answer 1 · 2016-10-03T16:57:44

$x=-9/7$

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!