Solve logarithmic equation: 2log_7(x+2)−log_7(3x+10)=0 Please, can someone check if this is the right answer x=−2+-sqrt(3x+10) Thank you.

Felix Fitzgerald

Felix Fitzgerald

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2022-08-22

Solve logarithmic equation: 2 log 7 ( x + 2 ) log 7 ( 3 x + 10 ) = 0
Please, can someone check if this is the right answer
x = 2 ± 3 x + 10
Thank you.

Answer & Explanation

g5riem7z

g5riem7z

Beginner2022-08-23Added 12 answers

Let's rewrite the equation.
2 log 7 ( x + 2 ) log 7 ( 3 x + 10 ) = 0 2 log 7 ( x + 2 ) = log 7 ( 3 x + 10 ) log 7 ( ( x + 2 ) 2 ) = log 7 ( 3 x + 10 ) ( x + 2 ) 2 = 3 x + 10
Now all we have to do is solve for x in that equation.
( x + 2 ) 2 = 3 x + 10 x 2 + 4 x + 4 = 3 x + 10 x 2 + x 6 = 0 ( x + 3 ) ( x 2 ) = 0
x = 3 ,   2
However only x = 2 is a solution, because 2 log 7 ( x + 2 ) is not defined for x = 3. Therefore the solution is:
x = 2
Hope I helped
bravere4g

bravere4g

Beginner2022-08-24Added 1 answers

log 7 ( x + 2 ) 2 log 7 ( 3 x + 10 ) = 0 log 7 ( x + 2 ) 2 ( 3 x + 10 ) = 0 x 2 + 4 x + 4 3 x + 10 = 1 x 2 + 4 x + 4 = 3 x + 10 x 2 + x 6 = 0
Solving for x will give you x = 3 and x = 2. But only 2 is acceptable as log 7 ( x + 2 ) is not defined for x = 3

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