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