Find the solution set of the equation log_x(3x-2)+log_(x^2)(1/(3x-2))=1

flatantsmu 2022-09-06 Answered
Find the solution set of the equation
log x ( 3 x 2 ) + log x 2 ( 1 3 x 2 ) = 1
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Answers (1)

Emilia Boyle
Answered 2022-09-07 Author has 10 answers
Given
log x ( 3 x 2 ) + log x 2 ( 1 3 x 2 ) = 1 log x ( 3 x 2 ) + 1 2 ( log x 1 log x ( 3 x 2 ) ) = 1 log x ( 3 x 2 ) + 1 2 ( 0 log x ( 3 x 2 ) ) = 1 log x ( 3 x 2 ) 1 2 log x ( 3 x 2 ) = 1 1 2 log x ( 3 x 2 ) = 1 log x ( 3 x 2 ) = 2 ( 3 x 2 ) = x 2 x 2 3 x + 2 = 0 x ( x 2 ) 1 ( x 2 ) = 0 ( x 1 ) ( x 2 ) = 0 x 1 = 0  or  x 2 = 0 x = 1  or  x = 2
but x 1 as x is in base and nase 1 x=2 is only solution.
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