ideally, we would match bases or whatnot
but we can't
tricky
ok so
remember
ln(a^x)=xln(a)
so
take ln of both sides
(4x-7)ln3=(2x+3)ln4
expand
4xln3-7ln3=2xln4+3ln4
remember that ln4=ln2^2, so 2xln4=2xln2^2=4xln2
minus 4xln2 from both sides and add 7ln3 to both sides
4xln3-4xln2=3ln4+7ln3
undistribute x
x(4ln3-4ln2)=3ln4+7ln3
remember that ln(a)-ln(b)=ln(a/b)
so 4ln3-4ln2=4(ln3-ln2)=4(ln(3/2))
divide both sides by (4ln(3/2))
x=[tex] \frac{3ln(4)+7ln(3)}{4ln( \frac{3}{2}) } [/tex]
and that 3ln4 is 3ln2^2 or 6ln2
x=[tex] \frac{6ln(2)+7ln(3)}{4ln( \frac{3}{2}) } [/tex]
