Question

A logarithmic equation:

Answer 1

\[\frac{ 1 }{ 2 } + \log_{3} \sqrt{x^{2}-4} = \log_{9} (5x)\]

Answer 2

Can someone tell me how I'm able to make the bases the same number?

Answer 3

There are 5-6 Rules of Logarithms (here on Openstudy there is a guy @ The Vipe who wrote them in excellent TUTORIAL - look at his nick)
What specifically you need is\[\log_{a^n} B = \frac{1}{n}\log_a B\]

Answer 4

So you can apply that on the RIGHT HAND SIDE to get\[\log_9 5x = \log_{3^2} 5x = \frac{1}{2}\log_35x\]

Answer 5

Oh, thanks!

Answer 6

Also, but on the left side [above - I meant @TheViper] you should rewrite\[1/2 = \log_3 \sqrt{3}\]

Answer 7

NOW YOU JAVE ALL THE TERMS IN THE SAME BASE - base 3

Answer 8

Thanks @shello130

Answer 9

Awesome, thanks! I just had trouble trying to figure out how to make the bases the same.

Answer 10

My advice - DO find @TheViper tutorial.

Answer 11

I will.

Answer 12

Thanks @dpaInc

Answer 13

yw...:)

Answer 14

@dpaInc What does "yw" shorthanding in modern talking ?

Answer 15

"You're welcome"

Answer 16

Thx @shello130