Logarithmic equation help log _5(x+3)+log _5(3x-5)=log _(25)(9x^2)

dripcima24

dripcima24

Answered question

2022-10-09

Logarithmic equation help
log 5 ( x + 3 ) + log 5 ( 3 x 5 ) = log 25 ( 9 x 2 )
I have the answer: { 181 1 6 } (only answer that falls in the domain)
i understand how to work with the left side but can't figure out how to get the RH side to base 5.

Answer & Explanation

Carson Mueller

Carson Mueller

Beginner2022-10-10Added 7 answers

Use the fact that 2 log 25 ( 9 x 2 ) = log 5 ( 9 x 2 ), which follows from
5 log 5 ( 9 x 2 ) = 9 x 2 = 25 log 25 ( 9 x 2 ) = 5 2 log 25 ( 9 x 2 ) .
Then the equation becomes 2 log 5 ( ( x + 3 ) ( 3 x 5 ) ) = log 5 ( 9 x 2 ) or log 5 ( ( ( x + 3 ) ( 3 x 5 ) ) 2 ) = log 5 ( 9 x 2 ). This means that ( ( x + 3 ) ( 3 x 5 ) ) 2 = ( 3 x ) 2 , hence ( x + 3 ) ( 3 x 5 ) = ± 3 x. I'm sure you can finish it from here.
charlygyloavao9

charlygyloavao9

Beginner2022-10-11Added 2 answers

We have log 25 b = 1 2 log 5 b. For the power to which we must raise 25 to get b is half the power to which we must raise 5 to get b

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