write each expression as a single logarithm in simplest form. state any restrictions on the variable.
write each expression as a single logarithm in simplest form. state any restrictions on the variable.
\(log_3\frac{\sqrt{x}}{x}+log_3\sqrt[5]{x^2}+\frac{3}{2}log_3x\)
\(=log_3\frac{\sqrt{x}\cdot \sqrt[5]{x^2}\cdot \sqrt{x^3}}{x}\)
\(=log_3(x^{\frac{1}{2}+\frac{2}{5}+\frac{3}{2}-1})\)
\(=log_3(x^{1.4})\)
\(=1.4\times log_3(x)\)
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