Examples of Changing From Logarithmic Form to Exponential Form To change from logarithmic form to exponential form, identify the base of the logarithmic equation and move the base to the other side of the equal sign. Moving the base will make the current number or variable into the exponent. Do not move anything but the base, the other numbers or variables will not change sides and the word “log” will be dropped.
Example – Write the logarithmic equation 5 = log9 x in exponential form. In this example, the base 9 moved from the right side of the equal sign to the left side of the equal sign turning 5 into the exponent. Example – Write the logarithmic equation x = log 3 16 in exponential form. In this example, the base 3 moved from the right side of the equal sign to the left side of the equal sign turning x into the exponent. Example – Write the logarithmic equation log x 22 = 18 in exponential form. In this example, the base x moved from the left side of the equal sign to the right side of the equal sign turning 18 into the exponent. Example – Write the logarithmic equation 13 = log y x in exponential form. In this example, the base y moved from the right side of the equal sign to the left side of the equal sign turning 13 into the exponent. Example – Write the logarithmic equation log 5 z = 67 in exponential form. In this example, the base 5 moved from the left side of the equal sign to the right side of the equal sign turning 67 into the exponent.