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)

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) =

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

⇒   (using ln(A) - ln(B) = )

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^