Question

Change the exponential statement to an equivalent statement involving a logarithm. 25 = 5²:

a) log5(25) = 2
b) log25(5) = 2
c) log2(25) = 5
d) log5(2) = 25

Answer 1

The exponential statement 25 = 5² can be rewritten in logarithmic form as log5(25) = 2, stating that the base 5 raised to the power of 2 equals 25.

Step-by-step explanation:

To change the exponential statement 25 = 5² to an equivalent statement involving a logarithm, we need to consider the base of the exponential expression, which is 5, and the exponent, which is 2. The logarithmic form of this expression will state that the logarithm of 25 to the base 5 equals 2. This is because logarithms answer the question: 'To what exponent must the base be raised in order to yield a certain number?'. Therefore, the correct statement is log5(25) = 2.

To change the exponential statement to an equivalent statement involving a logarithm, you need to use the property that states 'The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.'

So, in this case, you want to express 25 as a logarithm. Since 5 raised to the power of 2 equals 25, the equivalent statement involving a logarithm is:

log5(25) = 2