Question

Solve 4 log12 2 + log12 x = log12 96
can someone please detail the steps needed to solve this problem?

Answer 1

have you covered logarithm rules yet?

Answer 2

that's what I'm working on right now, but I just cant seem to get this one on my own

Answer 3

here's a log rules sheet --> http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif
we'll first use the 3rd rule listed there, for the exponent, and then the 1st rule, for the factors

Answer 4

\(\bf {\color{red}{ 4}}log_{12}(2) + log_{12}(x) = log_{12}(96)
\\ \quad \\
log_{12}(2^{\color{red}{ 4}}) + log_{12}(x) = log_{12}(96)
\\ \quad \\
log_{12}(2^{\color{red}{ 4}}\cdot x)= log_{12}(96)\implies log_{12}(16x)= log_{12}(96)
\\ \quad \\
\textit{since both sides are at }log_{12}\textit{ we can just remove that}
\\ \quad \\
16x=96\)

Answer 5

awesome!!! that's what I got on my paper. thank you for the chart :)

Answer 6

yw