Question

Write the expression as a single logarithm.
Express powers as factors.
**open question to see the rest of the problem**

Answer 1

\[(a.) \log_{6} \sqrt{x}-\log_{6}x^3 \]

\[(b.) 4\log_{a}(6x^8)-\frac{ 1 }{ 3 }\log_{a}(8x+15) \]

Answer 2

@jim_thompson5910

Answer 3

for the first one, you'll use the rule

\[\Large \log_{b}(x)-\log_{b}(y)=\log_{b}\left(\frac{x}{y}\right)\]

Answer 4

so what do you get when you use that for part a?

Answer 5

\[\frac{ \sqrt{x} }{ x^3}\]

Answer 6

no wait it'd be \[\log_{6} \frac{ \sqrt{x} }{ x^3 }\]

Answer 7

@jim_thompson5910

Answer 8

correct

Answer 9

for part b, you have to use this rule first

\[\Large y\log_{b}(x)=\log_{b}(x^{y})\]

Answer 10

and then you can use the rule you used on part a)

Answer 11

I put in \[\log_{6}\frac{ \sqrt{x} }{ x^3 } \] and it says it's wrong...

Answer 12

ok try to simplify \[\Large \frac{\sqrt{x}}{x^3}\]

Answer 13

use the idea \[\Large \sqrt{x} = x^{1/2}\] and subtract exponents

Answer 14

what do you mean "subtract the exponents"?

Answer 15

you'll have

\[\Large \frac{\sqrt{x}}{x^3} = \frac{x^{1/2}}{x^3}\]

Answer 16

subtract the exponents 1/2 and 3

Answer 17

ohhh so that's be -5/2?

Answer 18

@jim_thompson5910