Question 250055
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