Condense the expression to a single logarithm using the properties of logarithms. \[ \log (x)-\frac{1}{2} \log (y)+6 \log (z) \] Enclose arguments of functions in parentheses and include a multiplication sign betw example, \( c^{*} \log (h) \).

Calculate or simplify the expression \( \log(x)-\frac{1}{2}\log(y)+6\log(z) \). Simplify the expression by following steps: - step0: Solution: \(\log_{10}{\left(x\right)}-\frac{1}{2}\log_{10}{\left(y\right)}+6\log_{10}{\left(z\right)}\) - step1: Add the terms: \(\log_{10}{\left(\frac{x}{y^{\frac{1}{2}}}\right)}+6\log_{10}{\left(z\right)}\) - step2: Use the logarithm base change rule: \(\log_{10}{\left(\frac{x}{y^{\frac{1}{2}}}\right)}+\log_{10}{\left(z^{6}\right)}\) - step3: Transform the expression: \(\log_{10}{\left(\frac{x}{y^{\frac{1}{2}}}\times z^{6}\right)}\) - step4: Multiply the terms: \(\log_{10}{\left(\frac{xz^{6}}{y^{\frac{1}{2}}}\right)}\) - step5: Simplify: \(\log_{10}{\left(\frac{xz^{6}\sqrt{y}}{y}\right)}\) The expression \[ \log (x)-\frac{1}{2} \log (y)+6 \log (z) \] can be condensed to a single logarithm using the properties of logarithms as follows: \[ \log (x)-\frac{1}{2} \log (y)+6 \log (z) = \log_{10}{\left(\frac{xz^{6}\sqrt{y}}{y}\right)} \]