solve for x

3log_(4)x+log_(4)2-log_(4)(x-2)

show steps if you can!

Question

solve for x 

3log_(4)x+log_(4)2-log_(4)(x-2)

show steps if you can!

anonymous · Answer

Can you please put it in the equation. I can't understand what it says.

anonymous · Answer

*equation?

mathstudent55 · Answer

$\Large 3 \log_4 x+ \log_4 2- \log_4 (x-2)$

anonymous · Answer

$$3\log_4x+\log_42-\log_4(x-2)$$

mathstudent55 · Answer

Is that what you meant?
There is no equal sign, so it is not an equation.
What do you need to do with it?
Write it as a single log? Or is the equal sign missing?

anonymous · Answer

the question just said "Simplify."

anonymous · Answer

I think I just need to write it as a single log since there is no equal sign.

mathstudent55 · Answer

Ok.
I think what that means is to write the entire thing as a single log.

mathstudent55 · Answer

You need to know these three rules of logs:

$\log a + \log b = \log ab$

$\log a - \log b = \log \dfrac{a}{b} $

$\log a^n = n \log a$

The third rule is not needed in this problem, but you need to know it.

anonymous · Answer

yeah, i have those in my notes.

mathstudent55 · Answer

Look only at the part in red below for now.
Use the first rule.
How do you combine that sum of logs into one single log?

$\Large \color{red}{3 \log_4 x+ \log_4 2}- \log_4 (x-2)$

mathstudent55 · Answer

BTW, I'm sorry, but you do need the third rule.
Use the rule of the exponent first on the first log.
Then combine the two red logs into one using the first rule.

mathstudent55 · Answer

Use the third rule (exponent) on the green log below.

$\Large \color{green}{3 \log_4 x} + \log_4 2- \log_4 (x-2)$

mathstudent55 · Answer

Can you complete the bottom equation below?
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