write the expression as a single logarithm.\n$6\\left(3\\log_{m}y - \\log_{m}w + \\frac{1}{18}\\log_{m}x\\rig…
write the expression as a single logarithm.\n$6\\left(3\\log_{m}y - \\log_{m}w + \\frac{1}{18}\\log_{m}x\\right)$\n$\\log_{\\square}(\\square)$
Answer
Explanation:
Step1: Apply power rule to logs
$\log_m y^3 - \log_m w + \log_m x^{\frac{1}{18}}$
Step2: Distribute the outer coefficient 6
$6\log_m y^3 - 6\log_m w + 6\times\frac{1}{18}\log_m x$ Simplify coefficients: $18\log_m y - 6\log_m w + \frac{1}{3}\log_m x$
Step3: Reapply power rule
$\log_m y^{18} - \log_m w^6 + \log_m x^{\frac{1}{3}}$
Step4: Combine logs using product/quotient rules
$\log_m\left(\frac{y^{18}x^{\frac{1}{3}}}{w^6}\right)$ or $\log_m\left(\frac{y^{18}\sqrt[3]{x}}{w^6}\right)$
Answer:
$\log_m\left(\frac{y^{18}x^{\frac{1}{3}}}{w^6}\right)$ (or equivalent form $\log_m\left(\frac{y^{18}\sqrt[3]{x}}{w^6}\right)$)