Question

Rewrite the logarithmic expression log(ab³) in equivalent logarithmic form. there may be more than one correct answer. a. log(a) log(b³)

b. log(a)(log(b))³
c. log(a) 3log(b)
d. (log(ab))³
e. 3log(ab)
f. none of the above

Answer 1

The expression log(ab³) can be rewritten as log(a) + 3log(b), using the properties of logarithms that deal with products and exponents.

Step-by-step explanation:

The logarithmic expression log(ab³) can be rewritten using the properties of logarithms. One property states that the logarithm of a product can be written as the sum of the logarithms, so log(ab³) = log(a) + log(b³). Another property tells us that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the base, giving us log(b³) = 3log(b). Combining these two, we get the equivalent logarithmic expression as log(a) + 3log(b), which matches option (c).