Help with logarithms?

Sep 2018
27
0
Philippines
Hello everyone. We've been given an assignment on logarithms and I've managed to answer everything except this one (please see attached picture). I don't know what to do with the 2log9(x-1)log9(x^2-x) part. Do I separate it with a + sign since that's the rule for logarithms being multiplied?

All help is much appreciated! Thank you very much in advance. :)
 

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ChipB

MHF Helper
Jun 2014
310
128
NJ
No, it is not true that log(a)log(b) = log(a) + log(b).

I think there is probably a typo in the problem statement. If instead of 2log(x-1)log(x^2-2) it had a minus sign: 2log(x-1)-log(x^2-x) then the problem works out nicely. Do you happen to have the answer for x?
 

Plato

MHF Helper
Aug 2006
22,491
8,653
No, it is not true that log(a)log(b) = log(a) + log(b).

I think there is probably a typo in the problem statement. If instead of 2log(x-1)log(x^2-2) it had a minus sign: 2log(x-1)-log(x^2-x) then the problem works out nicely. Do you happen to have the answer for x?
I agree & had reached the same correction: $2\log(x-1)-\log(x^2-1)=\log\left(\dfrac{(x-1)^2}{(x^2-1)}\right)=\log\left(\dfrac{(x-1)}{(x+1)}\right)$
 
Dec 2016
306
167
Earth
No, it is not true that log(a)log(b) = log(a) + log(b).

I think there is probably a typo in the problem statement. If instead of 2log(x-1)log(x^2-x) [greg1313 edit] it had a minus sign: 2log(x-1)-log(x^2-x) then the problem works out nicely.
x = -4/5 would not be a solution to the revised problem with the inserted minus sign, because the logarithm of the second argument
with it substituted makes it undefined. Speaking closer about the base/parent function, f(x) = 2log(x) has a domain of x > 0, while
g(x) = log(x^2) has a domain of x equals all real numbers, except 0.
The hypothetical revised problem has no real solution.
 
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Sep 2018
27
0
Philippines
Hi everyone. Thank you all for the replies. :) Our teacher said that the revised version is actually supposed to have a positive sign in between the two logarithms.
 
Apr 2008
230
48
Beer soaked ramblings follow.
Hi everyone. Thank you all for the replies. :) Our teacher said that the revised version is actually supposed to have a positive sign in between the two logarithms.
Do us all a favor and post the exact problem statement?
 
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