I'm having problems with these equations in particular:
(logx^1/2)-(logx^1/3)=log2
and
log(base4)(x+2)+log(base4)(x-3)=log(base4)9
Thanks.
Focus on the left of the equal sign. When you subtract logs, and they have like bases, you may divide what you are taking the log of.
So:
Now the logs cancel, and you're left with:
Now cube both sides:
That simplifies to:
Square both sides, and so is 64.
Plug it back in to make sure it's correct.
Once again, focus on the left side of the equal sign. When you add logs with like bases, you may multiply what you are taking the log of.
So:
Logs cancel:
Use the quadratic formula.
I got
Check to see if both solutions work.