Question

Write the exponential equation 5^3 = 125 in its logarithmic form.

a) log_5 125 = 3
b) log_3 125 = 5
c) log_{125} 5 = 3
d) log_5 3 = 125

Answer 1

The exponential equation 5^3 = 125 is written in logarithmic form as log_5 125 = 3.The exponential equation 5^3 = 125 can be written in its logarithmic form as log₅ 125 = 3. This means that the exponent 3 is the logarithm of 125 to the base 5.

Step-by-step explanation:

The exponential equation 5^3 = 125 can be written in its logarithmic form by understanding that logarithms are the inverse operations of exponentials. When the equation is taking the form a^b = c, where 'a' is the base, 'b' is the exponent, and 'c' is the result, we write this in logarithmic form as log_a c = b. Therefore, using this formula, the logarithmic form of the given exponential equation is log_5 125 = 3. This means the power to which the base 5 must be raised to get 125 is 3, matching option a).