Problem

Solve the given problem. If $x=\ln 3$ and $y=\ln 2$, express $\ln 36$ in terms of $x$ and $y$. \[ \ln 36= \]

Solution

Step 1 :Given that $x=\ln 3$ and $y=\ln 2$, we are asked to express $\ln 36$ in terms of $x$ and $y$.

Step 2 :We know that $36 = 2^2 * 3^2$. Therefore, we can express $\ln 36$ as $\ln (2^2 * 3^2)$.

Step 3 :Using the properties of logarithms, we can simplify this expression to $2\ln 2 + 2\ln 3$.

Step 4 :Since $x=\ln 3$ and $y=\ln 2$, we can substitute these values into the expression to get $2y + 2x$.

Step 5 :\(\boxed{\ln 36 = 2x + 2y}\)

From Solvely APP
Source: https://solvelyapp.com/problems/17181/

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