Use the properties of logarithms to CONDENSE the expression.
\[
3 \ln 2+4 \ln x-\ln 5-2 \ln y=
\]
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Answer

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Answer

So, the condensed form of the given expression is \(\boxed{\ln \left(\frac{8x^4}{5y^2}\right)}\)

Steps

Step 1 ：Apply property 1 to the given expression: \(3 \ln 2+4 \ln x-\ln 5-2 \ln y = \ln 2^3 + \ln x^4 - \ln 5 - \ln y^2\)

Step 2 ：Simplify the expression: \(\ln 2^3 + \ln x^4 - \ln 5 - \ln y^2 = \ln 8 + \ln x^4 - \ln 5 - \ln y^2\)

Step 3 ：Apply properties 2 and 3 to the expression: \(\ln 8 + \ln x^4 - \ln 5 - \ln y^2 = \ln \left(\frac{8x^4}{5y^2}\right)\)

Step 4 ：So, the condensed form of the given expression is \(\boxed{\ln \left(\frac{8x^4}{5y^2}\right)}\)