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Ok thats the exact answer i got but the r answer sheet says -ln2/ln3

Yeah, there's a careless mistake :(((

x = ln2/ln3 does not satisfy the original equation.

x = -ln2/ln3 satisfies the original equation.

in the working on the left, mistake is in 4th line from bottom. the "+ln3" should be "-ln3" due to the '-' sign outside the bracket in the previous line.