Homework 3 1 intro to logarithms answer key

As you just learned, logarithms reverse exponents. For this reason, they are very helpful for solving exponential equations. For example the result for can be given as a logarithm, . You will learn how to evaluate this logarithmic expression over the following lessons.

The only problem is that if instead of 3 it was a fraction, there would be a negative number under the square root. This is usually avoided because it becomes more complicated because we must use imaginary numbers to find the answer. Because of this there are no negative bases in logarithms.

From the change of base theorem, log base a of b = (ln b)/ (ln a). For example, you can calculate log base 3 of 5 by calculating (ln 5)/ (ln 3) which should give approximately 1.465. (Note that if your calculator also has a log key, another way to calculate log base 3 of 5 is to calculate (log 5)/ (log 3).

When rewriting an exponential equation in log form or a log equation in exponential form, it is helpful to remember that the base of the logarithm is the same as the base of the exponent. In the following problems, you will convert between exponential and logarithmic forms of equations.