Question

Solve 3^(x – 4) = 7^(x + 9)

Answer 1

start with
\[(x-4)\ln(3)=(x+9)\ln(7)\] then a bunch of algebra to solve for \(x\)

Answer 2

@satellite73 ok? would the answer be x ≈ –25.86

Answer 3

i have no idea, you have to do some algebra first

Answer 4

@satellite73 I'm stuck on the algebra, can you help me work it out?

Answer 5

remember that \(\ln(3)\) and \(\ln(7)\) are just numbers

Answer 6

distribute first
\[\ln(3)x-4\ln(3)=\ln(7)x+9\ln(7)\]

Answer 7

then put everything with an \(x\) on one side, everything else on the other
\[\ln(3)x-\ln(7)x=9\ln(7)+4\ln(3)\]

Answer 8

factor the \(x\) on the left
\[\left(\ln(3)-\ln(7)\right)x=9\ln(7)+4\ln(3)\]

Answer 9

then divide
\[x=\frac{9\ln(7)+4\ln(3)}{\ln(3)-\ln(7)}\]

Answer 10

i have no idea what this number is, now is when you use a calculator

Answer 11

\(x\approx-25.855890260549890173158545490824\)