Question

Logarithim help?? (PIC INSERTED)

Answer 1

@whpalmer4

Answer 2

We' ll rearrange the equation to get all the logs on 1 side, and the numbers on the other.

\[\log_5(x+3) -1 = -\log_5(x+7)\]\[\log_5(x+3) + \log_5(x+7) = 1\]Remember that adding the logarithms of two quantities is the same as taking the logarithm of the product:

\[\log_5((x+3)(x+7)) = 1\]Raise 5 to each side to get rid of the log:
\[5^{\log_5((x+3)(x+7))} = 5^1\]simplify
\[(x+3)(x+7) = 5\]\[x^2+7x+3x+21 = 5\]\[x^2+10x + 16 = 0\]Now solve that for \(x\). You'll get two solutions, but only 1 makes sense (the other would cause us to take a logarithm of a negative number, which we don't want).