Help with logarithms?

kaonashi

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
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
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: $2\log(x-1)-\log(x^2-1)=\log\left(\dfrac{(x-1)^2}{(x^2-1)}\right)=\log\left(\dfrac{(x-1)}{(x+1)}\right)$

greg1313

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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kaonashi

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.

jonah

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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