Question

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

Answer 1

3^(4x-7)=4^(2x+3)

ln(3^(4x-7))=ln(4^(2x+3))

4xln(3)-7ln(3)=ln(4^(2x+3))

4xln(3)-7ln(3)-2xln(4)=3ln(4)

2x(2ln(3)-ln(4))=7ln(3)+3ln(4)

\[2x=\frac{7\ln(3)+3\ln(4)}{2\ln(3)-\ln(4)}\]
\[x=\frac{7\ln(3)+3\ln(4)}{2(2\ln(3)-\ln(4))}\]

Answer 2

x=0.6166

Answer 3

thank you. so you used ln to solve it, but i dont understand how you substituted or set up the equation.

Answer 4

@evisabello nothing was substituted ...
He took ln( ) of both sides and used the property \[\ln(y^r)=r \ln(y) \]
Then he used the distributive property a(b+c)=ab+ac on both sides!
Then he put all of his terms with the factor x on one side and all the terms without the factor x on the other side.
Then the side with terms that included x, he factored x out and divided by the junk next to the x on both sides.