Question

help step by step please on how to do this

Answer 1

\[2^{3x+1}=3^{x-2}\]

Answer 2

\[(3x+1)\ln2=(x-2)\ln{3}\]
\[3x\ln{2}+\ln{2}=x\ln{3}-2\ln{3}\]

Answer 3

Can you do the rest now?

Answer 4

take the natural log of both sides to get
ln(2)^(3x+1)=ln(3)^(x-2)
there is a property of logs that lets you do this:
(3x+1)ln(2)=(x-2)ln(3)
distribute to get
3xln2+ln2=xln(3)-2ln(3)
now just solve with algebra:
x(3ln2-ln3)=-2ln(3)-ln2
x=(-2ln3-ln2)/(3ln2-ln3)

Answer 5

thanks yeh