Question

Simplify: 2log3(3x) - log3(x2)

--> I got it to log3(3x^2) - log3(x^2) but now what?

Answer 1

Okay so:
Basic log properties -->
1.) \[\log_{a}x-\log_{a}y=\log_{a}\frac{ x }{ y } \]

\[2\log_{3}(3x)-\log_{3}(x^2) \]
=
\[2\log_{3}\frac{ 3x }{ x^2 } \]

Answer 2

@stephanieelizzz ...
how could you simplify this further?

Answer 3

careful @stephanieelizzz

you need to square ALL of 3x. Not just the x

it should be (3x)^2 = 9x^2 instead of just 3x^2

Answer 4

@sunnnystrong you need to move the 2 up into the exponent before you can use that rule

Answer 5

@jim_thompson5910 ooops okay haha

\[\log_{3}\frac{ 9x^2 }{ x^2 }\]

Answer 6

@jim_thompson5910 oopsiesssss thank you!

Answer 7

Can you cancel out the x^2? @sunnnystrong

Answer 8

@jim_thompson5910 thank you!

& Yes I would think soo hmmm not 100%.
What do you think @jim_thompson5910 ?

Answer 9

yes the x^2 terms will cancel. Then you need to evaluate \(\Large \log_3(9)\)

Answer 10

You'd end up with 2 after everything is said and done, I believe. :)

Answer 11

yep since 9 = 3^2