Thread: 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. 2^x+3=3^x-4
2. log₇(x+1)³=2
3. 3000=2000(1.01)^​4t

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.

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.

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.

ok so i need to make the 2 and 3 the same Utilizing the change of base rule?

Yes, since you have two different bases.

so i have log(x+3)/log2=log(x-4)/log3 ?

No it's even simpler than that: recall that log_a(a^y) = y * log_a(a) = y.