SOLUTION: How do you condense this expression into a logarithm of a single quantity? 7[In z + In(z+7)]-6 In(z-5)= ??? I thought the answer would be something like this: In((x^(-6)/

Question 626769: How do you condense this expression into a logarithm of a single quantity?
7[In z + In(z+7)]-6 In(z-5)= ???
I thought the answer would be something like this:
In((x^(-6)/(z+7)*(z-5))^(7))
My answer automatically comes out to be wrong, though. I'm not sure how to answer this one. Please help me. Thank you!
- Cassidy
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Side note: Those are lowercase L's and not uppercase i's. So it's Ln (for natural log). I'm going to use uppercase L's for emphasis

7[Ln z + Ln(z+7)]-6 Ln(z-5)

7*Ln(z(z+7))-6*Ln(z-5)

7*Ln(z^2+7z)-6*Ln(z-5)

Ln((z^2+7z)^7)-Ln((z-5)^6)

Ln[ ((z^2+7z)^7/((z-5)^6) ]

So the answer is $\ln\left(\frac{(z^2+7z)^{7}}{(z-5)^{6}}\right)$

--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------
RELATED QUESTIONS
4[ln z+ln(z+5)]−4ln(z−4) I need to condense this expression to the... (answered by nerdybill)

Condense the expression to the logarithm of a single quantity. 7 log4 x + 5 log4 y... (answered by josmiceli)

Hello! How do I condense this expression to a single quantity? 7/6ln(z-9) + ln(z) (answered by Edwin McCravy)

Condense the expression to the logarithm of a single quantity 2 ln(6) + 2... (answered by jim_thompson5910)

How do you condense this expression to a logarithm of a single quantity?... (answered by fcabanski)

Condense the expression to the logarithm of a single quantity. 2 ln 5 + 2 ln... (answered by lynnlo)

condense the expression to the logarithm of a single quantity. 2 ln(6) + 2 ln(z �... (answered by MathLover1)

Condense the expression to the logarithm of a single quantity. (3/2) ln (z-2) + ln... (answered by stanbon)

How do I condense this expression to a single logarithm? {{{ log z+log x / 3 + log y /... (answered by lwsshak3)