Question

Convert the exponential expression 5^3 = 125 into 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

Final Answer:

The exponential expression
`5^3` = 125 into its logarithmic form is 3.

The correct answer is a)
`log_5` 125 = 3

Step-by-step explanation:

To convert the exponential expression
`5^3` = 125 into its logarithmic form, it is expressed as log base 5 of 125 equals 3. This logarithmic representation highlights the power to which the base (5) must be raised to yield the given result (125).

In logarithmic notation, the base (in this case, 5) is the number being raised to a certain power, and the result (here, 3) is the exponent. So,
`log_5` 125 = 3 signifies that 5 raised to the power of 3 equals 125.

Understanding logarithmic forms is crucial in mathematical applications, especially in solving equations involving exponents and exponential growth or decay.

The correct answer is a)
`log_5` 125 = 3