Question

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

numbers.
ln(x) + 2 ln(y) − 3 ln(z)

Answer 1

`\ln(xy^2)/(z^3)`

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(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(xy^2)/(z^3)` (using ln(A) - ln(B) =
`\ln(A)/(B)` )