Alan G. answered • 07/14/16
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Alex,
Are you trying to expand the logarithm?
log5 (a2b3/25) = 2 log5 a + 3 log5 b - 2.
If you do not already know that a and b are both positive, then they should have absolute values. In order to find log5 b, you need to know that it is positive to begin with, but in your question, a could be any nonzero number.
Remember, to find ANY logarithm of a number, IT MUST BE A POSITIVE NUMBER!
If you did not want to expand the logarithm, then you would definitely need to have b positive in order for the problem to even make sense. Since a2 will be positive as long as a in not zero, you need do nothing about a in this case.
In the future, please be a little more careful about what you ask, because some of these questions are subtle and I cannot give you a quick explanation without having you state the problem carefully. Logarithms are difficult at first and I do not want to intentionally discourage you.
Alan G.
Alex,
Just remember that you cannot find a logarithm of any number which is NOT positive. Your teacher may have been referring to another type of problem, but I cannot be sure without knowing exactly what wa said in your class.
√a2 = |a|, while 3√a3 = a, for a any real number is what I was thinking. This has nothing to do with logarithms, though.
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07/14/16
Alex C.
07/14/16