# Three logarithm, questions I would appreciate explained

• Dec 6th 2012, 07:19 PM
AwkwardRaven
Three logarithm, questions I would appreciate explained
Hello I have three logarithm questions, I would very much appreciate it if someone could explain how to solve them, thank you.

1. 2x+3=3x-4
2. log7(x+1)3=2
3. 3000=2000(1.01)​4t
• Dec 6th 2012, 07:42 PM
chiro
Re: Three logarithm, questions I would appreciate explained
Hey AwkwardRaven.

What log laws (and exponential laws) have you been taught?

Also you should show us any partial attempts you have taken because it shows effort on your part and it makes our job which is to help you much easier.
• Dec 6th 2012, 07:52 PM
AwkwardRaven
Re: Three logarithm, questions I would appreciate explained
The properties of logarithms and the change of base rule.

for #1 I tried: log2(x+3)=log2(x-4) but after that I'm kind of stuck. I'm not sure how to separate the x from the +3 and -4.
• Dec 6th 2012, 08:00 PM
chiro
Re: Three logarithm, questions I would appreciate explained
That is in-correct: you should use the fact that log_a(b) = log_x(b)/log_x(a) where x and a are bases.

From this you get x+3 = (x-4)/log_2(3) and you can re-arrange to get x.
• Dec 6th 2012, 08:03 PM
AwkwardRaven
Re: Three logarithm, questions I would appreciate explained
ok so i need to make the 2 and 3 the same Utilizing the change of base rule?
• Dec 6th 2012, 08:06 PM
chiro
Re: Three logarithm, questions I would appreciate explained
Yes, since you have two different bases.
• Dec 6th 2012, 08:33 PM
AwkwardRaven
Re: Three logarithm, questions I would appreciate explained
so i have log(x+3)/log2=log(x-4)/log3 ?
• Dec 6th 2012, 08:43 PM
chiro
Re: Three logarithm, questions I would appreciate explained
No it's even simpler than that: recall that log_a(a^y) = y * log_a(a) = y.