Question

What is ln x + 2 ln y − ln z written as a single logarithm.

Answer 1

Answer:

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

Step-by-step explanation:

Given expression:

$\ln x+2\ln y-\ln z$

To write the given expression in single logarithm.

Solution:

We will apply the logarithm properties to write the expression in single logarithm.

We have:

$\ln x+2\ln y-\ln z$

Using power rule : [ $a\ln b= \ln b^a$ ]

⇒ $\ln x+\ln y^2-\ln z$

Using product rule: [ $\ln a+\ln b=\ln ab$ ]

⇒ $\ln xy^2-\ln z$

Using quotient rule. [ $\ln a - \ln b = \ln\frac{a}{b}$ ]

⇒ $\ln \frac{xy^2}{z}$

Thus, we successfully converted the expression to a single logarithm expression.