Solving Logarithmic Equations Worksheet (Page 4 of 8) in pdf

Solving Logarithmic Equations Worksheet Page 4

Here is another example, solve ln(4x 1) 3.

- =

ln(4x 1) 3

- =

This problem does not need to be simplified because there

is only one logarithm in the problem.

4x 1 e

- =

Rewrite the problem in exponential form by moving the

base of the logarithm to the other side. For natural

logarithms the base is e.

Simplify the problem by cubing e. Round the answer as

4x 1 20.085537

- »

appropriate, these answers will use 6 decimal places.

5.271384

Solve for x by adding 1 to each side and then dividing each

side by 4.

Check the answer; this is an acceptable answer because we

5.271384

get a positive number when it is plugged back in.

Therefore, the solution to the problem ln(4x 1) 3

- = is x ≈ 5.271384.

Now that we have looked at a couple of examples of solving logarithmic equations containing terms without

logarithms, let’s list the steps for solving logarithmic equations containing terms without logarithms.

Steps for Solving Logarithmic Equations Containing Terms without Logarithms

Step 1: Determine if the problem contains only logarithms. If so, stop and use Steps for Solving

Logarithmic Equations Containing Only Logarithms. If not, go to Step 2.

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 in exponential form.

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 Worksheet Page 4