Precalculus Examples

$\frac{\log (57)}{56 \log (7 \csc (\frac{4.9}{\sqrt{78}}))}$

Step 1

Rewrite $\log (7 \csc (\frac{4.9}{\sqrt{78}}))$ as $\log (7) + \log (\csc (\frac{4.9}{\sqrt{78}}))$ .

$\frac{\log (57)}{56 (\log (7) + \log (\csc (\frac{4.9}{\sqrt{78}})))}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{78}$ as $78^{\frac{1}{2}}$ .

$\frac{\log (57)}{56 (\log (7) + \log (\csc (\frac{4.9}{78^{\frac{1}{2}}})))}$

Step 3

Divide $1$ by $2$ .

$\frac{\log (57)}{56 (\log (7) + \log (\csc (\frac{4.9}{78^{0.5}})))}$

Step 4

Raise $78$ to the power of $0.5$ .

$\frac{\log (57)}{56 (\log (7) + \log (\csc (\frac{4.9}{8.83176086})))}$

Step 5

Divide $4.9$ by $8.83176086$ .

$\frac{\log (57)}{56 (\log (7) + \log (\csc (0.55481574)))}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $\log (57)$ as $\log (3 (19))$ .

$\frac{\log (3 (19))}{56 (\log (7) + \log (\csc (0.55481574)))}$

Step 6.2

Rewrite $\log (3 (19))$ as $\log (3) + \log (19)$ .

$\frac{\log (3) + \log (19)}{56 (\log (7) + \log (\csc (0.55481574)))}$