Question

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. (2 points) 4log x + 3log y

Answer 1

4log(x) x + 3log(y)

The power rule of logarithms states:

log(4)^X = Xlog(4)

The product rule of logarithms states:

log(x) + log(y) = log(xy)

Rewrite each logarithm using the power rule of logarithms:

4log(x) = log(x)^4

3log(y) = log(y)^3

log(x)^4 + log(y)^3

Combine them using the product rule of logarithms:

log(x)^4 + log(y)^3 = log(x^4y^3)

Answer:

log(x^4y^3)