Question

Solve: 3^4x-7=4^2x+3

Answer 1

I think you mean to say
3^(4x-7)=4^(2x+3)
correct me if i'm wrong...

Answer 2

Yes, that is what I meant to ask.

Answer 3

So take ln( ) of both sides! :)

Answer 4

Then you will be able to bring the exponents down using ln(x^r)=rln(x)
this property!

Answer 5

\[(4x-7) \ln(3)=(2x+3) \ln(4)\]
Now distribute and ...
Put every term with x on one side and
every term without x on the other side

Answer 6

\[4 \ln(3) x -7 \ln(3)=2 \ln(4) x+3 \ln(4)\]
this is the part where you do the:
"Put every term with x on one side and
every term without x on the other side"

Answer 7

Would you like to try to finish this?
You can use the draw tool if you want to show me how to finish this and I can fix where you went wrong.

Answer 8

or go wrong*

Answer 9

I'm having a bit of trouble with the "Put every term with x on one side and every term without x on the other side." What exactly does this mean?

Answer 10

how do you solve
2x+1=3x-1

2x-3x=-1-1

see i put every term with x on one side
and every term without x on the other

Answer 11

Oh, I get that. But what do you do once you move the x's onto the one side and the non x's onto the other?

Answer 12

going from the example I just wrote
x(2-3)=-1-1

Then divide both sides by (2-3)
x=(-1-1)/(2-3)

Answer 13

in others word you are going to factor out that x
and you will have x(junk)=something

Answer 14

\[4 \ln(3) x -7 \ln(3)=2 \ln(4) x+3 \ln(4) \]
So here is where I left you...

Answer 15

so one possible way to go about this is to subtract 2 ln(4) x on both sides
then add 7 ln(3) on both sides

Answer 16

Ohhh! I got it! The answer is 7.305... Thanks soooo much for your help! :)

Answer 17

Awesome! I'm glad you got it.