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log 2x - log 5 = 1
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High School Teacher
To solve log2x - log5 = 1
We know that 1 = log10. Therefore,
log2x -log5 = log 10
lo2x = log10 +log5
log2x = log(10*5), as loga +logb = log(ab).
log2x = log50. Take antilogarithms
2x = 50
2x/2 = 50/2
Posted by neela on July 30, 2010 at 1:00 PM (Answer #1)
We'll add log 5 both sides:
log 2x - log 5 + log 5 = 1 + log 5
log 2x = log 10 + log 5
We'll use the product property, for the sum from the right side:
log 2x = log 50
We'll subtract log 50 both sides:
log 2x - log 50 = 0
We'll use the quotient property of the logarithms:
log 2x/50 = 0
2x/50 = 10^0
We'll cross multiply:
2x = 1*50
We'll divide by 2:
x = 25
Since x is positive, the equation has the solution x=25.
Posted by giorgiana1976 on July 31, 2010 at 3:13 AM (Answer #2)
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