Problem

Write the logarithmic expression as a single logarithm with coefficient 1 , and simplify as much as possible. Assume that the variables represent positive real numbers. \[ \ln y+\ln 5=\square \] \begin{tabular}{ccc} \hline$ㅁ i n$ & $\square^{\square}$ & 믐 \\ $x$ & 5 \\ \hline \end{tabular} Check Save For Later Submit A

Solution

Step 1 :The given expression is \(\ln y + \ln 5\).

Step 2 :From the properties of logarithms, the sum of two logarithms with the same base is equivalent to the logarithm of the product of the numbers.

Step 3 :Therefore, we can simplify the given expression by combining the two logarithms into one, which would be \(\ln (y*5)\) or \(\ln (5y)\).

Step 4 :The simplified logarithmic expression is \(\boxed{\ln (5y)}\).

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