Question

Write each expression as a single logarithm. 4log(x-2) + 7log(x).

a. log((x-2)⁴x⁷)
b. log((x-2)⁷x⁴)
c. log((x-2)⁴) + log(x⁷)
d. log((x-2)⁴) - log(x⁷)

Answer 1

To write each expression as a single logarithm, we can simplify using the properties of logarithms.

Step-by-step explanation:

To write each expression as a single logarithm, we can use the properties of logarithms. Let's simplify each expression:

a. 4log(x-2) + 7log(x) = log((x-2)⁴) + log(x⁷) = log((x-2)⁴x⁷)

b. 4log(x-2) + 7log(x) = log((x-2)⁴) + log(x⁷) = log(x⁷(x-2)⁴)

c. 4log(x-2) + 7log(x) = log((x-2)⁴) + log(x⁷)

d. 4log(x-2) - 7log(x) = log((x-2)⁴) - log(x⁷)