Question

¿How to solve with logarithms?

See image please

Answer 1

Explanation:

Apply the natural log to both sides we have

`(-(2/3)x -1 ) \ln 2 = (3-2x)\ln 3\\-x(2/3)\ln 2 + 2x\ln 3 = 3\ln 3 -\ln 2\\x\left((-2)/(3)\ln 2 +2\ln 3\right)=\ln (27/2)\\x\left(\ln 9 -\ln √(8)) =\ln(27/2)\\\\x\ln (9/√(8))=\ln(27/2)\\\\x= \ln(27/2) / \ln(9/√(8))`