Simplify/Condense

$\ln (x) + \ln (y x)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (x (y x))$

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

$\ln (x \cdot x y)$

Step 2.2

Multiply $x$ by $x$ .

$\ln (x^{2} y)$

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Exponential and Logarithmic Functions

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$