Since the bases on both sides are the same, we can use the one-to-one property to set the exponents equal to each other and
solve!
Solve for in the following exponential equation:
.
Practice solving exponential equations
How You Can (And Should) Get More Practice!
Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.
Theoretically Easier Difficulty Problem
Theoretically Medium Difficulty Problem
We need the bases on both sides are the same, so we can use the one-to-one property to set the exponents equal to each
other and solve. To do this, we should rewrite one of the bases as a power of the other base (which way doesn’t
matter)
Try rewriting the right hand side’s base. Instead of we could write it as . Don’t forget the parentheses!
Solve for in the following exponential equation:
.
Theoretically Harder Difficulty Problem
We need the bases on both sides are the same, so we can use the one-to-one property to set the exponents equal to each other
and solve. To do this, we will need to find a common base that can be raised to a power to get the bases on either side (but it’s
unlikely that one side is a direct power of the other).
You can replace the base on the lefthand side by: , and the base on the righthand side by: . Don’t forget the
parentheses!
Solve for in the following exponential equation:
.