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Solve the following logarithm equation: log(2x) = log 5 + log(x – 6)
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We have to solve: log(2x) = log 5 + log(x – 6)
log(2x) = log 5 + log(x – 6)
use the property log a + log b = log (a*b)
=> log(2x) = log (5*(x – 6))
Now we can equate 2x and 5(x - 6)
2x = 5(x - 6)
=> 2x = 5x - 30
=> 3x = 30
=> x = 30/3
=> x = 10
The solution of the equation is x = 10
Posted by justaguide on November 3, 2011 at 12:12 PM (Answer #1)
You may move the terms in x to the left side and then you could use the property of quotient of logarithms having same bases.
log (2x)-log(x-6)=log 5
Use quotient property: log u-log v=log (u/v)
log (2x)-log(x-6)=log [(2x)/(x-6)]
The bases of logarithms are the same and the logarithmic function is injective, therefore (2x)/(x-6)=5
Subtract 5 both sides=>
Add terms from numerator:
The solution is approved because the only value that is not allowed for x is x=6 because the denominator of the fraction (2x-5x+30)/(x-6) must not be zero.
Posted by sciencesolve on November 3, 2011 at 7:57 PM (Answer #2)
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