Determine if the following statement is true or false. the logarithm of a power is equal to the product of the exponent of the power and the logarithm of the base of the power

False. Logarithms is just another name for"exponent". The log of a product is equal to the SUM of the exponents of the factors.

For this case we are going to write the logarithm in its generic form:
 f (x) = loga (x) ^ b
 By properties of logarithm we have:
 f (x) = b * loga (x)
 
 True,
 The logarithm of a power is equal to the product of the exponent of the power and the logarithm of the base of the power