Answer:
[tex]\ln\frac{xy^2}{z^3}[/tex]
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) = [tex]\ln\frac{A}{B}[/tex]
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
⇒ [tex]\ln\frac{xy^2}{z^3}[/tex] (using ln(A) - ln(B) = [tex]\ln\frac{A}{B}[/tex] )
