When the variable we want to solve for is in the exponent, we again
"do the same thing" to both sides of the equation. This time we take
logarithms, using the property that
is also useful.
For each, we solve for x
. Notice how we use the log(x
) functions to eliminate base 10 and base e
exponentials, respectively, and how we use the logarithm rule for
Note that this solution is exact. The decimal approximation
gives an approximate solution.
Note that we divided both sides by two before taking the log to
make life easier for ourselves.
Note that we could solve this with the base 10 log as well:
Check with your calculator that these two answers are the
Be sure you've gone through each step in the examples above before
doing these. Once you've worked them until you're sure that you
understand them, go on to the next section. There are more problems
of this type in the section test at the end of the section.
Note that you can get new practice problems by clicking the "Refresh"
button at the bottom of the practice set.
precal: 7.5 - solving exp eqns
page created: Tue May 21 22:47:13 2013
©2003-2007 Gavin LaRose, Pat Shure /
University of Michigan Math Dept. /
Regents of the University of Michigan