# Logarithms homework question

1. ### moe11

8
1. The problem statement, all variables and given/known data
12^x=4X8^(2x)

Big X= multiplication sign
little x= unknown

i simply cannot figure this out. Any help please?

2. Relevant equations
4.6X1.06^(2x+3)=5X3^(x)

2. ### Dick

25,914
Re: logarithms!

Use logarithms! Isn't that your title? Take the log of both sides and use the rules of logarithms to simplify. What do you get?

3. ### moe11

8
Re: logarithms!

i wouldnt post this if i could do it as easily as you said. Can you explain? Thats why i'm here.

4. ### Dick

25,914
Re: logarithms!

log(12^x)=log(4*8^(2x)). That wasn't so hard. Now simplify it. Use rules of logarithms like, log(a*b)=log(a)+log(b), log(a^b)=b*log(a).

5. ### HallsofIvy

41,269
Staff Emeritus
Re: logarithms!

Since you titled this "logarithms", Dick assumed you knew some basic rules of logarithms. Take the logarithm of both sides: log(12x= log((4)82x)

Now use the fact that log(ab)= log(a)+ log(b) and that log(ax)= x log(a).