Solve. log_a x+ log_a(x-2)=log_a(x+4)

stratsticks57jl

stratsticks57jl

Answered question

2022-07-28

Solve.
log a x + log a ( x 2 ) = log a ( x + 4 )

Answer & Explanation

gutsy8v

gutsy8v

Beginner2022-07-29Added 14 answers

Since log ( A ) + log ( B ) = log ( A B ), we can write the left-hand side as log ( x ( x 2 ) ).
Since all of these are log base a, we can raise both sides to the power of a, giving:
x(x-2) = x+4
x 2 2 x = x + 4
x 2 3 x + 4 = 0
(x-4)(x+1) = 0
so our candidate solutions are x = 4, x = -1. But we know x=-1 is not a valid solution since we can't take the log of a negative number.
Freddy Friedman

Freddy Friedman

Beginner2022-07-30Added 5 answers

Solve
log a x + log a ( x 2 ) = log a ( x + 4 )
log a x ( x 2 ) ) = log a ( x + 4 )
x*(x-2) = x+4
x 2 2 x = x + 4
x 2 3 x 4 = 0
(x-4)(x+1)=0
x=4 or x=-1 is not solution
x= 4 solution

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?