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

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.

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.

Re: Solving simple logarithmic equations

Best is to use the rule

which works for any base.

Simplify what you get and then use the same process as for the first one.

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