Question

Write the following sum as a single logarithm. Assume all variables are positive. log3(2) + log (2 + 4) = The answer format in lowercase characters is: log_base (number) Spaces in the answer are optional.

Answer 1

$\\\mathrm{Solution}\\ \\ \mathrm{log_{_3}\left(x\right)+log_{_3}\left(x+4\right)}\\ \\ \mathrm{\mathrm{Apply\:log\:rule}:\quad \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)}\\ \\ \mathrm{\log _3\left(x\right)+\log _3\left(x+4\right)=\log _3\left(x\left(x+4\right)\right)}\\ \\ \mathrm{=\log _3\left(x\left(x+4\right)\right)}\\ \\$