Question

Find the solution to the equation 64^(3 + x) = 4^2x.

Answer 1

64^(3 + x) = 4^2x.

Answer 2

x= -9

Answer 3

We have
\[64^{(3+x)}=4^{2x}\]
We know \(64=4^3\)
so
\[(4^3)^{3+x}=4^{2x}\]
We have now
\[4^{9+3x}=4^{2x}\]
Equating the powers of 4 both sides, we get
\[9+3x=2x\]
subtract both sides by 9
\[3x=2x-9\]
subtract both sides by 2x, we get
\[x=-9\]