Question

Solve the logarithmic equation 2^3x-2 =3^2x-1

Answer 1

$$2^{3x-2} =3^{2x-1}$$

$$\ln (2^{3x-2})=\ln (3^{2x-1})$$

$$(3x-2)\ln (2)=(2x-1)\ln (3)$$

$$x(3\ln (2)-2\ln(3))=2\ln (2)-\ln(3)$$

$$x=\dfrac{\ln(8/9)}{\ln(4/3)}$$