Question

Condense the following logarithmic expression.

2 ln(x) + 5 ln(y) - 7 ln(z) - In (5)
Answer:

Answer 1

ln(x²y⁵/(5z⁷))

Explanation:

You want to condense the logarithmic expression 2 ln(x) + 5 ln(y) - 7 ln(z) - In (5).

Rules of logarithms

The relevant rules of logarithms are ...

a·ln(b) = ln(b^a)

ln(ab) = ln(a) +ln(b)

ln(a/b) = ln(a) -ln(b)

Application

`2ln((x))+5ln((y))-7ln((z))-ln((5))=\boxed{\ln\left((x^2y^5)/(5z^7)\right)}`