Question

Solve correct to four decimal places: 3^x =4^(x-7)
What do I do since the bases are not the same?

Answer 1

Take the log of both sides.

Answer 2

a raft of algebra

Answer 3

start with
\[\ln(3)x=(x-7)\ln(4)\] and then solve for \(x\)

Answer 4

don't be confused, \(\ln(3)\) and \(\ln(4)\) are just some constants (numbers)

Answer 5

you got the algebra?

Answer 6

Would I divide log(3) from both sides?

Answer 7

I canceled the logs on both sides and ended up with
3x= 4x-14
x=14