# Solving simple logarithmic equations

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• Dec 16th 2012, 12:47 PM
Huggakhan
Solving simple logarithmic equations
I missed a whole week of math class and I'm totally lost. I learn best through examples and working my way back from answers through trial and error.

how would I solve for logx16 = 2/3 (with x being the base)... I rewrote it as X^2/3 = 16 but don't know where to go from there... Thanks in advance, I'm sure this is a really simple answer.

And, log(base x)(1/81)=-4
• Dec 16th 2012, 12:50 PM
BobP
Re: Solving simple logarithmic equations
So far so good.
Now remove the fractional power by raising both sides to the power three and then taking square roots.
• Dec 16th 2012, 01:10 PM
Huggakhan
Re: Solving simple logarithmic equations
Yes, I did that and I got the answer.

For the next one I also got the answer, but I don't know if my process is correct.
• Dec 16th 2012, 01:17 PM
BobP
Re: Solving simple logarithmic equations
Best is to use the rule

$\displaystyle \displaystyle \log\left(\frac{a}{b}\right)=\log a - \log b,$ which works for any base.

Simplify what you get and then use the same process as for the first one.
• Dec 16th 2012, 04:49 PM
bjhopper
Re: Solving simple logarithmic equations
Quote:

Originally Posted by Huggakhan
I missed a whole week of math class and I'm totally lost. I learn best through examples and working my way back from answers through trial and error.

how would I solve for logx16 = 2/3 (with x being the base)... I rewrote it as X^2/3 = 16 but don't know where to go from there... Thanks in advance, I'm sure this is a really simple answer.

And, log(base x)(1/81)=-4

log Bx (1/81)=-4
x^-4 = 1/81
1/x^4 =1/81
x^4 =81
x=3