a What property allows you to rewrite a sum of two same-base logarithms?
B
b What property allows you to rewrite the difference of two same-base logarithms?
A
aProduct Property of Logarithms or Power Property of Logarithms
B
bQuotient Property of Logarithms
Practice makes perfect
a We want to rewrite the expression log_4 5 + log_4 5 as a single logarithm. For this we can use the Product Property of Logarithms, since this property allows us to rewrite the sum of two same-base logarithmic expressions as the logarithm of the product of their arguments.
Alternatively, we can start by adding their coefficients since they are like terms. Then we can use the Power Property of Logarithms. Recall that this property allows us to rewrite the product of a constant and a logarithmic expression as the logarithm of the argument raised to said constant.
As we can see, both ways are equally fast and get the same result.
b Now we will rewrite the expression log_5 4 - log_5 6 as a single logarithm. For this we can use the Quotient Property of Logarithms, since this property allows us to rewrite the difference of two same base logarithmic expressions as the logarithm of the quotient of their arguments.
