138k views
0 votes
What is ln x + 2 ln y - ln z written as one logarithm?

What is ln x + 2 ln y - ln z written as one logarithm?-example-1
User Lis
by
8.3k points

1 Answer

4 votes

Hello there. To solve this question, we have to remember some properties about logarithms.

Given the expression:


\ln(x)+2\ln(y)-\ln(z)

We want to rewrite it as a single logarithm.

For this, remember the following rules:


\begin{gathered} \log_a(b)+\log_a(c)=\log_a(b\cdot c) \\ \\ \log_a(b)-\log_a(c)=\log_a\left((b)/(c)\right) \\ \\ c\cdot\log_a(b)=\log_a(b^c) \end{gathered}

In this case we apply the third rule to the middle logarithm in order to get:


\ln(x)+\ln(y^2)-\ln(z)

Apply the first and second rules


\begin{gathered} \ln(xy^2)-\ln(z)\text{ \lparen First rule\rparen} \\ \\ \Rightarrow\ln\left((xy^2)/(z)\right)\text{ \lparen Second rule\rparen} \end{gathered}

This is the answer to this question and it is contained in the first option.

User Nicolas Othmar
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.