Question 250055: explain is the difference between a logarithm of a product and the product of logarithm and give example of each.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! logarithm of a product would be:
log(x*y)
product of a logarithm would be:
log(x)*log(y), or it would more likely be:
x * log(y)
I've seen x * log(y) before, but haven't seen log(x) * log(y).
That doesn't mean it doesn't exist. It just means that I haven't seen it.
I have seen log(x) / log(y) before. That's more common.
Some examples:
EXAMPLE OF LOGARITHM OF A PRODUCT
equation is y = 2.773 * 3.402
take log of both sides to get:
log(y) = log(2.773 * 3.402)
this is equivalent to:
log(y) = log(2.773) + log(3.402)
solve for log(y) to get:
log(y) = .974684179
solve for y to get:
y = 9.433746
multiply 2.773 * 3.402 to get:
y = 9.433746
Answers are the same as they should be.
EXAMPLE OF PRODUCT OF A LOGARITHM
y = 7.434^(2.3)
take log of both sides to get:
log(y) = log(7.434^(2.3)
this becomes:
log(y) = 2.3 * log(7.434)
solve for log(y) to get:
log(y) = 2.003811881
solve for y to get:
y = 100.8815812
solve y = 7.434^(2.3) directly using your calculator to get:
y = 100.8815812
Answers are the same as they should be.
EXAMPLE OF DIVISION OF A LOGARITHM
5000 = 2^x
take log of both sides to get:
log(5000) = log(2^x)
this becomes:
log(5000) = x * log(2)
divide both sides by log(2) to get
x = log(5000)/log(2)
solve for x to get:
x = 12.28771238
plug x into original equation to get:
5000 = 2^12.28771238 = 5000
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