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Another approach: 2log4(2x-3)=4. Divide by 2: log4(2x-3)=2.
Write in exponential form: log4(2x-3)=2 becomes 42=2x-3.
log4(2x-3) = 2 [Divided both sides by 2]
4log4(2x-3) = 42 [Raised everything as exponents to 4]
2x-3 = 16 [ 4log4a = a, 42=16]
Solve for x