Logarithm where 0<a<1/2. Find x Given that log_a(3x-4a)+ log_a(3x)=2/(log_2a)+ log_a(1-2a) where 0<a<1/2. find the value of x.

Amiya Melendez 2022-10-13 Answered
Logarithm where 0 < a < 1 2 . Find x
Given that log a ( 3 x 4 a ) + log a ( 3 x ) = 2 log 2 a + log a ( 1 2 a ) where 0 < a < 1 2 . find the value of x
I got the attempt until x = 2 ( a + ( a 1 ) 2 3 and 2 ( ( a 1 ) 2 a ) 3 .
How to proceed to find x?
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Answers (1)

indyterpep
Answered 2022-10-14 Author has 12 answers
So, let's use log's with base a.
log a ( 3 x ( 3 x 4 a ) ) = 2 log a 2 + log a ( 1 2 a ) ,
and
3 x ( 3 x 4 a ) = 4 ( 1 2 a ) .
Solve it and
x = 2 3 , x = 4 a 2 3 .
But for second x, 3 x 4 a = 2, and log is undefined. So, you have x = 2 / 3.
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