Question

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

Answer 1

michele

Answer 2

@Michele_Laino help

Answer 3

x=16 yes

Answer 4

here, if we apply the properties of logarithms, we can rewrite the left side as below:
\[\Large \begin{gathered}
{\log _2}{2^2} + {\log _2}{6^2} - {\log _2}3x = {\log _2}\left( {\frac{{4 \times 36}}{{3x}}} \right) = \hfill \\
= {\log _2}\left( {\frac{{144}}{{3x}}} \right) \hfill \\
\end{gathered} \]

Answer 5

more fractions

Answer 6

furthermore, we have:
\[\Large 3 = {\log _2}8\]

Answer 7

x=16 not right

Answer 8

your equation, can be rewritten as below:
\[\Large {\log _2}\left( {\frac{{144}}{{3x}}} \right) = {\log _2}8\]

Answer 9

so, using the uniqueness of logarithm we have to solve this equation:
\[\Large \frac{{144}}{{3x}} = 8\]
what is x?

Answer 10

oh no i don't know how to do this fraction michele

Answer 11

we have to multiply both sides by 3x, so we get:
\[144 = 24x\]

Answer 12

6!

Answer 13

that's right!

Answer 14

good!

Answer 15

thanks!

Answer 16

i got 100% !!!

Answer 17

ok! :):)