Use the properties of logarithms to expand $\log \left(z x^{2}\right)$.
Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.
\[
\log \left(z x^{2}\right)=\square
\]
$\square \log \square \quad \frac{\square}{\square}$
$x$
S
Answer
So, the expanded form of the given logarithmic expression is \(\boxed{2 \log (x)+\log (z)}\)
Step 1 ：Given the logarithmic expression \(\log \left(z x^{2}\right)\)
Step 2 ：Using the properties of logarithms, we can expand this expression. The property \(\log(ab) = \log(a) + \log(b)\) allows us to separate the variables \(z\) and \(x^2\)
Step 3 ：So, \(\log \left(z x^{2}\right) = \log(x^2) + \log(z)\)
Step 4 ：We still have an exponent in the term \(\log(x^2)\). We can use the property \(\log(a^n) = n\log(a)\) to remove this exponent
Step 5 ：Applying this property, we get \(2\log(x) + \log(z)\)
Step 6 ：So, the expanded form of the given logarithmic expression is \(\boxed{2 \log (x)+\log (z)}\)
