(log x)^3= log x^3

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
darovitz
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Joined: Sat Jul 17, 2010 11:05 pm
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(log x)^3= log x^3

How do I solve this problem: (log x)^3= log x^3

car.man
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Joined: Tue Mar 24, 2009 6:18 pm

Re: (log x)^3= log x^3

Do a log rule to get the power on the right outside of the log.
http://www.purplemath.com/modules/logrules.htm

then move that log to the left, and factor.
logx(log2x-3)=0
http://www.purplemath.com/modules/simpfact.htm

solve the 2 factors.
http://www.purplemath.com/modules/solvelog.htm

write back if you get stuck

TJB
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Re: (log x)^3= log x^3

How do I see how to solve this? I do not see where to get the information. Thanks for any input.

TJB
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Joined: Sun Jul 17, 2016 11:27 am
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Re: (log x)^3= log x^3

This is still not very clear to me. The first step does not even make sense to me. Then how do you even factor a log? Any help is appreciated.

maggiemagnet
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Joined: Mon Dec 08, 2008 12:32 am
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Re: (log x)^3= log x^3

How do I see how to solve this? I do not see where to get the information.
Try studying the lessons at the links the other poster gave you:
Do a log rule to get the power on the right outside of the log.
http://www.purplemath.com/modules/logrules.htm
1. This first step explains that you need to apply the power-versus-multiplier rule to the log expression on the right-hand side of the equation, moving the power "3" from inside "log(x^3)", converting it to being a multiplier outside of, and in front of, the log expression.
then move that log to the left...
2-a. The second step starts with moving the expression from the right-hand side of the equation over to the left-hand side of the equation. You learned how to do this back in beginning algebra, when you learned how to solve linear equations (lesson); that is, you subtract it from both sides.
...and factor.
logx(log2x-3)=0
http://www.purplemath.com/modules/simpfact.htm
2-b. The second step continues with factoring. Since you have one log that has three copies (being cubed) and another that has one copy (and is multiplied by 3), you can factor one copy of "log(x)" out front. The poster gave you the final result of this step.
3. The third step is to use what you learned back when you studied solving quadratic equations (lesson); that is, when a factored form is equal to zero, then you can solve by setting each of the factors equal to zero.

After you have read the lessons at the links, please try to do the exercise, following the step-by-step instructions. If you still don't understand the first step (the log rules), then you may need to consider hiring a tutor in your area who can help you figure out what is missing in your background that is not letting you make any sense of your book, your instructor, or online lessons. Once that gap is found and filled, I'll bet you'll do great!