Solve log x + 3 log 2 = log 2/x
Answers
Answer:
1/2
Step-by-step explanation:
log x + 3 log 2 = log 2/x
log x + 3 log 2 = log 2 - logx
2log x + 3 log 2 = log 2
2log x = -2log 2
logx = log(1/2)
x = 1/2
HOPE YOU UNDERSTAND
Answer:
x = 9
Explanation:
log ( x − 3 ) + log ( x − 2 ) = log ( 2 x + 24 ) log ( ( x − 3 ) ( x − 2 )
= log ( 2 x + 24 ) ( x − 3 ) ( x − 2 )
= 2 x + 24
Simplify the left side:
x 2 − 3 x − 2 x + 6 = 2 x + 24 x 2 − 5 x + 6
= 2 x + 24
Add 5 x on both sides of the equation:
x 2 − 5 x + 6 + 5 x = 2 x 24 + 5 x x 2 + 6 = 7 x + 24
Move everything to the left side of the equation so that we can factor: x 2 + 6− 7 x − 24 = 0
x 2 − 7 x − 18 = 0
To factor this, we have to find two numbers that:
Add up to − 7
Multiply up to − 18
from ( 1 ⋅ − 18 )#
So we have to find a pair of factors of − 18
that add up to − 7 .
We know that the factors of − 18 are: − 18 , − 9 , − 6 , − 3 , − 2 , − 1 , 1 , 2 , 3 , 6 , 9 , 18 .
The two factors that add up to − 7 are − 9 and 2 .
So the factored form becomes: ( x − 9 ) ( x + 2 ) = 0
So ,
x − 9 = 0 and x + 2 = 0
x = 9 and x = − 2
However, these are not our final solutions! We must check our work when solving log equations by plugging it back into the original equation, since you cannot have a log of 0 or anything negative.
Let's check our first solution, x
= 9 : log ( 9 − 3 ) + log ( 9 − 2 )
= log ( 2 ( 9 ) + 24 ) log 6 + log 7
= log ( 18 + 24 ) log ( 6 ⋅ 7 )
= log42
= log 42
This is true! That means that
x = 9 .
Now let's check x
= − 2 : log ( − 2 − 3 ) + log ( − 2 − 2 )
= log ( 2 ( − 2 ) + 24 ) log ( − 5 ) + log ( − 4 )
= log ( − 4 + 24 )
Oh no! We cannot take the log of a negative number, but − 5 and − 4
are negative! That means that
x = − 2 is NOT a solution.
Finally, the answer is
x = 9 .
Hope this helps!
Step-by-step explanation:
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