To express log216=4 in exponential form, we write 24 = 16. For log5125=3, it would be 53 = 125. These conversions allow us to understand how to move between logarithmic and exponential forms.
The student's questions involve converting logarithmic equations into exponential form. In the logarithmic equation log216 = 4, we express it in exponential form by raising the base (2) to the power on the right side of the equation (4), to get the number inside the log (16). Thus, the exponential form is 24 = 16. Similarly, for log5125 = 3, we write it in exponential form as 53 = 125.
The steps to convert from logarithmic to exponential form involve knowing that logbA = C translates into bC = A. Understanding this conversion allows us to work with growth models, as well as simplifies calculations involving powers and roots. Remember that the logarithm tells us what power we need to raise the base to get the number.