Question

Write the following exponential equation as a logarithmic equation: 5^3=125

A) log_5 (125)=3
B) log_1 (255)=3
C) ln 5^3=125
D) log_3 (125)=5

Answer 1

The correct logarithmic form of the exponential equation 5^3=125 is log_5 (125)=3, as it represents the power to which 5 must be raised to obtain 125.

Step-by-step explanation:

To write the exponential equation 5^3=125 as a logarithmic equation, we need to understand that the base of the exponential function becomes the base of the logarithm, the exponent becomes the number the logarithm is equal to, and the result of the exponential expression is the number inside the logarithm. Therefore, we transform the given exponential equation into the logarithmic form:

log5 (125) = 3

This means that the power to which we must raise 5 to obtain 125 is 3. This is represented in logarithmic form where the base 5 corresponds to the base of the exponent in the original expression, and 3 is the exponent itself. This can be verified using the property where the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

From the options given, option A is correct: A) log5 (125)=3.