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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
Start by using an appropriate base on both sides of the equality to eliminate the logarithm.
In this case, you want to use as a base on both sides, so your first step looks like:
The exponential and the log undo each other, and on the other side of the equality you can compute the explicitly.
Solve for in the following logarithmic equation:
The sum of solutions is: .
Theoretically Medium Difficulty Problem
Start by using an appropriate base on both sides of the equality to eliminate the logarithm.
In this case, you want to use as a base on both sides, so your first step looks like:
The exponential and the log undo each other, and on the other side of the equality you can compute the explicitly.
From this point you proceed as normal, solving the polynomial by getting everything on the same side and factoring.
Solve for in the following logarithmic equation:
The sum of solutions is: .
Theoretically Harder Difficulty Problem
Start by using an appropriate base on both sides of the equality to eliminate the logarithm.
In this case, you want to use as a base on both sides, since both log bases can be raised to a power to get this number, which
makes things easier. So your first step looks like:
The exponential and the log undo each other, and on the other side of the equality you can compute the explicitly (via changing
the base into to a power, or by using the change of base formula if needed).
From this point you proceed as normal, solving the polynomial by getting everything on the same side and factoring.
Precalculus Algebra