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\frac{2\log_{2}\left(x\right)+3\log_{2}\left(y\right)}{3}
Factor out \frac{1}{3}.
\frac{2\ln(x)+3\ln(y)}{\ln(2)}
Consider 2\ln(x)\times \frac{1}{\ln(2)}+3\ln(y)\times \frac{1}{\ln(2)}. Factor out \frac{1}{\ln(2)}.
\frac{2\ln(x)+3\ln(y)}{3\ln(2)}
Rewrite the complete factored expression.