Question

Can someone help me with this?
2 log2 2 + 2 log2 6 − log2 3x = 3 is the equation. I'm new to logs, and I just tried out the problem. Here's what I did...
2 log2 2 + 2 log2 6 − log2 3x = 3
log2 4 + log2 36 - log2 3x = 3
4 + 36 - 3x = 3
40 - 3x = 3
-3x = -37
x = 12 1/3
However... I know this is incorrect. Since the answer choices are
x = 2
x = 6
x = 16
x = 18

Please don't give me the answer, I need to know how to do it.

Answer 1

\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\\:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}

Answer 2

Uh, I didn't see that in the lesson. What do I do with the ∞?

Answer 3

whoops wrong 1 sorry

Answer 4

can u type the equation correct plz

Answer 5

144 / 3x = 2^3 = 8
144/8 = 3x
18 = 3x

Answer 6

here this should help bro

Answer 7

step 1) use the power formula of logarithms: x logb (a) = logb a^x: so, 2 log2 (2) + 2 log2 (6) - log2 (3x) = 3 becomes log2(2^2) + log2 (6^2) - log2 (3x) = 3

step 2) simplify: log2 (4) + log2 (36) - log2 (3x) = 3

step 3) use the product rule of logarithms: logb (a) + logb (c) = logb (ac). So, log2 (4) + log2 (36) - log2 (3x) = 3 becomes log2 (36*4) - log2 (3x) =3

step 4) simplify: log2 (144) - log2 (3x) = 3

step 5) use the quotient rule of logarithms: logb (a) - logb (c) = logb (a/c). So, log2 (144) - log2 (3x) = 3 becomes log2 (144/3x) = 3

step 6) transform the logarithmic equation into an exponential one: logb (x) = y is the same as b^y=x
So, log2 (144/3x) = 3 becomes 2^3 = 144/3x

step 7) Simplify: 8 = 144/3x

step 8) multiply both sides by 3x: 3x*8 = (144/3x)*3x

step 9) simplify: 24x = 144

step 10) divide both sides by 24 and simplify: 24x/24 = 144/24
the answer should be 6.

Answer 8

does this help u any bro

Answer 9

@usercode3rror Yeah, thanks! Sorry, my internet went out for a bit.