The problem involves expanding a logarithmic expression into a sum and difference of logs. The expression given is log [ ( 2x^4(x-15)^3) / (12 sqrt (x^4-16) ].
Some participants are questioning the clarity of the original expression and the notation used. Others are exploring how to properly apply logarithmic properties to expand the expression fully. There is a recognition that further steps are needed to achieve complete expansion.
There are mentions of potential misunderstandings regarding the use of parentheses and the representation of exponents. Participants are also noting the importance of clarity in mathematical expressions to avoid confusion.
Some clarification, please. The numerator of what you wrote islolilovepie said:Homework Statement
Completely expand as a sum/difference of logs
log [ ( 2x^4(x-15)^3) / (12 sqrt (x^4-16) ]
lolilovepie said:Homework Equations
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)
Mark44 said: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.
Mark44 said: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 said: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)]