Log to exponential

Log to Exponential How is this possible?

By Mrs. Rapp

The Problem

Change the following equation into exponential form.

5 A = log B + 4 8 Notice it does not specify to solve for a variable but to put into Exponential Form.

How do we approach?

5 A = log B + 4 8 To place in exponential form, isolate log B by using the properties of equality.

This means whatever we do to one side of the equation, we must do to the other until log B is alone on one side.

Step 1 It may help you to think of log B as a group by placing parentheses around.

5 A = ( log B) + 4 8

Step 2 Always undo addition or subtraction first.

So move the + 4 to the opposite side using the opposite operation, which is subtraction.

5 A = ( log B) + 4 8 −4 −4 5 A − 4 = ( log B) 8

Step 3 Notice the left side has 2 terms. To remember they stay together, place parentheses around.

5 ( A − 4 ) = ( log B ) 8 This step is optional but often helps with future steps.

Fractions‌Yuk! The log B is being multiplied by a fraction. You have several options on how to handle this.

Option 1: Divide by the fraction.

Option 2: Multiply by the reciprocal.

Option 3: Multiply by the denominator to eliminate the fraction. Then divide.

If you are not a fan of fractions, I recommend Option 3. This is the option I will show.

Step 4 Undo the fraction by multiplying both sides by the denominator, which is 8 for this example.

5 ( A − 4 ) = (log B) 8 5 8 ( A − 4 ) = ( log B) ⋅ 8 8 8 ( A − 4 ) = 5 ( log B)

Step 5 Isolate log B by dividing by the coefficient, which is 5.

8 ( A − 4 ) = 5 ( log B) 5

5

8 ( A − 4) = ( log B) 5

Step 6 Now that log B is alone, remove the parentheses.

8 ( A − 4) = log B 5

Because no base is written, we know the base is understood to be 10. Often writing this helps with the final step.

8 ( A − 4) = log B 10 5

Step 7 To change from logarithmic form to exponential form, remember The base of the log is the base of the exponent.

Whatever the log equals becomes the exponent.

Whatever you take of the log of is what the exponential equals.

8 ( A − 4) = log B 10 5 B = 10

8( A−4 ) 5

Summary Group the log so it’s clear what you need to isolate before changing to exponential form.

Undo any addition or subtraction.

Undo any multiplication or division.

If no base, LOG has a base of 10 and LN has a base of e.

Change to exponential form.