Solve the equation. log_4(8x) - log_4(x - 1)= 2

Karsyn Beltran 2022-08-01 Answered
Solve the equation.
log 4 ( 8 x ) log 4 ( x 1 ) = 2
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Answers (2)

Izabelle Frost
Answered 2022-08-02 Author has 13 answers
log 4 ( 8 x ) log 4 ( x 1 ) = 2 remember log ( a / b ) = log ( a ) log ( b )
log 4 ( 8 x x 1 ) = log 4 4 2 log b ( b m ) = m log b ( b ) = m
8 x x 1 = 16
8x= 16x -16
8x=16
x=2
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yasusar0
Answered 2022-08-03 Author has 3 answers
Solve the equation.
log 4 ( 8 x ) log 4 ( x 1 ) = 2
Use the law of logarithm: log a ( A B ) = log a A log a B, to combine the logarithms.
log 4 ( 8 x x 1 ) = 2
Use the definition of the logarithmic function: log a x = y a y = x, to put the equation in exponential form.
4 2 = 8 x x 1
16 = 8 x x 1
Now solve for x.
16 ( x 1 ) = 8 x multiply both sides by (x-1).
16x-16=8x
16x-8x=16
8 x = 16 x = 16 8
So, x=2.
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