Question

Michele
Solve 4 log12 2 + log12 x = log12 96.

Answer 1

@Michele_Laino

Answer 2

x=12 yes

Answer 3

michele

Answer 4

here we can rewrite the left side as below:
\[\Large \begin{gathered}
4{\log _{12}}2 + {\log _{12}}x = {\log _{12}}{2^4} + {\log _{12}}x = \hfill \\
= {\log _{12}}16 + {\log _{12}}x = {\log _{12}}\left( {16x} \right) \hfill \\
\end{gathered} \]

Answer 5

yes x=12 good

Answer 6

thank michele

Answer 7

use the log laws for powers

here is an example

\[alog(b) = \log(b^a)\]

this is the 1st thing you need to do with the 1st term...

then simplify it

Answer 8

Solve 2 log2 2 + 2 log2 6 –log2 3x = 3

michele this

Answer 9

please wait

Answer 10

your equation becomes:
\[{\log _{12}}\left( {16x} \right) = {\log _{12}}1296\]

Answer 11

then use the log law for multiplication

\[\log(a) + \log(b) = \log(ab)\]

that needs to be used for both terms on the left hand side

Answer 12

then you will have 2 log terms with the same base that can be equated and solved

Answer 13

can i be right x=12

Answer 14

no, I think that is not the right answer

Answer 15

no its not 12.... read the information and equate the expressions

16x = 96

solve for x

Answer 16

96 is right michele?

Answer 17

using the uniqueness of logarithm we have to solve this equation:
\[16x = 96\]

Answer 18

so what is:
96/16=...?

Answer 19

fraction this time again!

Answer 20

6

Answer 21

yes! that's right!

Answer 22

good

Answer 23

one more michele thank

Answer 24

thanks!

Answer 25

ok!