Question

Write each expression as an equivalent expression with a single logarithm. Assume xx, yy, and zz are positive real

Answer 1

Answer:

$\ln\frac{xy^2}{z^3}$

Step-by-step explanation:

Data provided:

ln(x) + 2 ln(y) − 3 ln(z)

Now,

From the properties of log function,

ln(A) + ln(B) = ln(AB)

n × ln(x) = ln(xⁿ)

and,

ln(A) - ln(B) = $\ln\frac{A}{B}$

applying the properties in the given equation

we get

⇒  ln(x) + 2 ln(y)  − 3 ln(z)

or

⇒ ln(x) + ln(y²) - ln(z³)            (using n × ln(x) = ln(xⁿ))

or

⇒ ln(xy²) - ln(z³)                    (using ln(A) + ln(B) = ln(AB) )

or

⇒ $\ln\frac{xy^2}{z^3}$   (using ln(A) - ln(B) = $\ln\frac{A}{B}$ )