1. ## Natural logarithm problem

The problem asks to "write the expression as one logarithm"
(-pi)Ln(y^2/x) - 2Lny + 1/2 Ln x^20 • y^18
here is what I've already tried, and I don't think this is the correct answer
sorry I don't know why it's showing up upside down

2. ## Re: Natural logarithm problem

Your instructor needs to learn to use parentheses.

$-\pi \ln\left(\dfrac{y^2}{x}\right) - 2\ln y + \dfrac{1}{2}\ln \left(x^{20}y^{18}\right) = \ln\left(x^{10+\pi}y^{7-2\pi}\right)$

Here is how I would do it. I would use negative exponents:

$-\pi\ln\left(\dfrac{y^2}{x}\right) = -\pi\ln(x^{-1}y^2) = \ln(x^{-\pi}y^{2\pi})$

This way, everything becomes addition rather than a combination of addition and division.

3. ## Re: Natural logarithm problem

Originally Posted by Pelican
The problem asks to "write the expression as one logarithm"
(-pi)Ln(y^2/x) - 2Lny + 1/2 Ln x^20 • y^18
here is what I've already tried, and I don't think this is the correct answer sorry I don't know why it's showing up upside down
If you cannot learn to post correctly, then think again.
\begin{align*}- \pi \log \left( {\frac{{{y^2}}}{x}} \right) - 2\log (y) + \frac{1}{2}\log \left( {{x^{20}}{y^{18}}} \right)&= - 2\pi \log (y) + \pi \log (x) - 2\log (y) + 10\log (x) + 9\log (y) \\&=(7 - 2\pi )\log (y) + (\pi + 10)\log (x) \end{align*}

4. ## Re: Natural logarithm problem

Basically, what Plato and I are saying is that your answer at the bottom (top?) is correct.