Precalculus Examples

$\log_{3} (7) \sqrt{x^{5}} + \log_{3} (7) \sqrt{y^{2}} - \log_{3} (7) \sqrt{3}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

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Step 1.1.1

Factor out $x^{4}$ .

$\log_{3} (7) \sqrt{x^{4} x} + \log_{3} (7) \sqrt{y^{2}} - \log_{3} (7) \sqrt{3}$

Step 1.1.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\log_{3} (7) \sqrt{{(x^{2})}^{2} x} + \log_{3} (7) \sqrt{y^{2}} - \log_{3} (7) \sqrt{3}$

Step 1.2

Pull terms out from under the radical.

$\log_{3} (7) (x^{2} \sqrt{x}) + \log_{3} (7) \sqrt{y^{2}} - \log_{3} (7) \sqrt{3}$

Step 1.3

Pull terms out from under the radical, assuming positive real numbers.

$\log_{3} (7) x^{2} \sqrt{x} + \log_{3} (7) y - \log_{3} (7) \sqrt{3}$

Step 2

Reorder factors in $\log_{3} (7) x^{2} \sqrt{x} + \log_{3} (7) y - \log_{3} (7) \sqrt{3}$ .

$x^{2} \log_{3} (7) \sqrt{x} + y \log_{3} (7) - \log_{3} (7) \sqrt{3}$