Properties

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Change of Base Property

Example

Solve the equation: ChangeOfBaseEx1-1

Step 1. If it is not possible to create a common base, use the inverse function (logs). When applying inverses to an equation, do the same operation on both sides of the equals sign.

ChangeOfBaseEx1-1
properties_correction

Step 2.
Use properties of logs to eliminate the exponent.

Use the Power to a Power Property to multiply the exponent (x) by the exponent (ChangeOfBaseEx1-3)
ChangeOfBaseEx1-2

Step 3.
Solve for x.

Use the Change of Base Property & divide.

ChangeOfBaseEx1-4
ChangeOfBaseEx1-5

x = 4.755 (using a calculator)

Therefore, ChangeOfBaseEx1-6