Solving Logarithmic Equations Worksheet (Page 3 of 8) in pdf

Solving Logarithmic Equations Worksheet Page 3

Steps for Solving Logarithmic Equations Containing Only Logarithms

Step 1: Determine if the problem contains only logarithms. If so, go to Step 2. If not, stop and use

the Steps for Solving Logarithmic Equations Containing Terms without Logarithms.

Step 2: Use the properties of logarithms to simplify the problem if needed. If the problem has

more than one logarithm on either side of the equal sign then the problem can be

simplified.

Step 3: Rewrite the problem without the logarithms.

Step 4: Simplify the problem.

Step 5: Solve for x.

Step 6: Check your answer(s). Remember we cannot take the logarithm of a negative number, so

we need to make sure that when we plug our answer(s) back into the original equation we

get a positive number. Otherwise, we must drop that answer(s).

Solving Logarithmic Equations Containing Terms without Logarithms

After observing that the logarithmic equation contains terms without logarithms, what is the next step? The

next step is to simplify the problem using the properties of logarithms and then to rewrite the logarithmic

problem in exponential form. After rewriting the problem in exponential form we will be able to solve the

resulting problem.

Let’s finish solving the problem

log (5x 7) 5

= from earlier.

This problem does not need to be simplified because there

log (5x 7) 5

is only one logarithm in the problem.

Rewrite the problem in exponential form by moving the

5x 7 2

+ =

base of the logarithm to the other side.

Simplify the problem by raising 2 to the fifth power.

5x 7 32

+ =

Solve for x by subtracting 7 from each side and then

x 5

dividing each side by 5.

Check the answer; this is an acceptable answer because we

x 5

get a positive number when it is plugged back in.

Therefore, the solution to the problem

log (5x 7) 5

= is x = 5.

Solving Logarithmic Equations Worksheet Page 3