If the range of a function is the set of all outputs for the functions, what is the range of an exponential function? Which will grow faster, y = 3*4^x or y = 5*5^x? If a logarithm is the inverse of an exponential, then If 3^x = 10, what is the log (base 3) of 10? If x^9 = 20, what is the log (base x) of 20?   Use the properties of logs to solve 3^x = 6

The identity of (a-b)^2+(a+b)^2 = 2(a^2+b^2) helped clean things up a lot. However, "ln" has to be used with "e" rather than "log." The answer was not accepted by the homework system with "log," and it does give a different value when computed. Perhaps it was thought that "e" was a variable here instead of Euller's number. Could you please make this correction to the answer for other students who may look at it? Thank you.

It is known that log4x = k. Given this information, write the expression log4(64x^5) in terms of k

How does the second to last step come about? How does "log(5^x/2) + log(5^1/2)" turn into "log (sq. rt of 55^x)?"