How Do You Solve Exponential Equations Using Logarithms?

[moe11]

Homework Statement

12^x=4X8^(2x)

Big X= multiplication sign
little x= unknown

i simply cannot figure this out. Any help please?

Homework Equations

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

 

[Dick]

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?

 

[moe11]

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?

i wouldn't post this if i could do it as easily as you said. Can you explain? Thats why I'm here.

 

[Dick]

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).

 

[HallsofIvy]

Your equation is 12<sup>x=(4)82x.

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).</sup>