# Completely expand as a sum/difference of logs

lolilovepie

## Homework Statement

Completely expand as a sum/difference of logs
log [ ( 2x^4(x-15)^3) / (12 sqrt (x^4-16) ]

## The Attempt at a Solution

log 2x^4(x-15)^3 - log 12 sqrt (x^4-16)
3 log 2x^4(x-15) - 1/2log 12 (x^4-16)

Last edited:

Mentor

## Homework Statement

Completely expand as a sum/difference of logs
log [ ( 2x^4(x-15)^3) / (12 sqrt (x^4-16) ]
Some clarification, please. The numerator of what you wrote is
2x4 * (x - 15)3.

If that isn't what you meant, please use parentheses or brackets to make it clearer.

## The Attempt at a Solution

log 2x^4(x-15)^3 - log 12 sqrt (x^4-16)
3 log 2x^4(x-15) - 1/3log 12 (x^4-16)

Some parentheses would make this more readable, as would the inclusion of = for things that are equal.

Also, sqrt(x) = x1/2, not x1/3.

lolilovepie
Some clarification, please. The numerator of what you wrote is
2x4 * (x - 15)3.

If that isn't what you meant, please use parentheses or brackets to make it clearer.

Some parentheses would make this more readable, as would the inclusion of = for things that are equal.

Also, sqrt(x) = x1/2, not x1/3.

1) yeah, that's what i meant to say, but i didn't know how to do the exponents

2) ok okay thanks! did I solve the problem right because i'm not very sure :\

Mentor
Starting here --
log [ ( 2x^4 * (x-15)^3) / (12 sqrt (x^4-16) ]
= log [ 2x^4 * (x-15)^3] - log[12 * (x^4-16)^(1/2)]
Can you continue?

Notice that I added * to indicate multiplication. I think that's what you intended, but am not sure.

There are some properties of logs that you either don't know or aren't using, such as log(AB) = log(A) + log(B), assuming both A and B are positive.

lolilovepie
Starting here --
log [ ( 2x^4 * (x-15)^3) / (12 sqrt (x^4-16) ]
= log [ 2x^4 * (x-15)^3] - log[12 * (x^4-16)^(1/2)]
Can you continue?

Notice that I added * to indicate multiplication. I think that's what you intended, but am not sure.

There are some properties of logs that you either don't know or aren't using, such as log(AB) = log(A) + log(B), assuming both A and B are positive.

after continuing would it be:

[log 2x^4 + log (x-15)^3] - [log 12 + log (x^4-16)^1/2]

and then use the power rule?

[4 log 2x + 3 log (x-15)] - [log 12 + 1/2 log (x^4-16)]

Homework Helper
Gold Member
after continuing would it be:

[log 2x^4 + log (x-15)^3] - [log 12 + log (x^4-16)^1/2]

and then use the power rule?

[4 log 2x + 3 log (x-15)] - [log 12 + 1/2 log (x^4-16)]

It's still not completely expanded.