Question

2log(4)3x+log(4) 5x = condense into a single logarithm :)

Answer 1

@rachie19

Answer 2

alog b=log b^a

Answer 3

use this property and tell me what you can say about the first term

Answer 4

Log43x^2

Answer 5

hint:
for example, according to the rule of @jango_IN_DTOWN we can write:
\[\huge 2{\log _4}\left( {3x} \right) = {\log _4}{\left( {3x} \right)^2}\]
furthermore, please apply the subsequent rule:
\[\huge {\log _4}A + {\log _4}B = {\log _4}\left( {A \cdot B} \right)\]

Answer 6

Ok thanks

Answer 7

So log15x^2. Or am I wrong?

Answer 8

we can write this:
\[\Large \begin{gathered}
2{\log _4}\left( {3x} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
{=\log _4}{\left( {3x} \right)^2} + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left( {9{x^2}} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left\{ {\left( {9{x^2}} \right) \cdot \left( {5x} \right)} \right\} = ...? \hfill \\
\end{gathered} \]

Answer 9

please continue

Answer 10

what is: \(\Large 9x^2 \cdot 5x=...?\)

Answer 11

45x*^2

Answer 12

Log(4)45x^2

Answer 13

45xcube

Answer 14

that's right!
we get:
\[\huge \begin{gathered}
2{\log _4}\left( {3x} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
{\log _4}{\left( {3x} \right)^2} + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left( {9{x^2}} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left\{ {\left( {9{x^2}} \right) \cdot \left( {5x} \right)} \right\} = {\log _4}\left( {45{x^3}} \right) \hfill \\
\end{gathered} \]

Answer 15

\[\huge \begin{gathered}
2{\log _4}\left( {3x} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
{\log _4}{\left( {3x} \right)^2} + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left( {9{x^2}} \right) + {\log _4}\left( {5x} \right) = \hfill \\
\hfill \\
= {\log _4}\left\{ {\left( {9{x^2}} \right) \cdot \left( {5x} \right)} \right\} = \hfill \\
\hfill \\
= {\log _4}\left( {45{x^3}} \right) \hfill \\
\end{gathered} \]