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Can I please get some help with this equation? Evaluate and simplify log of csc(5pi/6) multiplied by csc(pi/4). Explain your work.

Can I Please Get Some Help With This Equation Evaluate And Simplify Log Of Csc5pi6 Multiplied By Cscpi4 Explain Your Work class=

Sagot :

1) Considering that the 1st property of Logarithms tells us:

[tex]\log _ab\text{ =c}\Leftrightarrow a^c=b[/tex]

2) Let's evaluate that:

[tex]\begin{gathered} \log _{\csc (\frac{5\pi}{6})}(\frac{\csc \pi}{4})=x\Rightarrow\csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \\ \csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \log \csc (\frac{5\pi}{6})^x=\log \csc (\frac{\pi}{4}) \\ \text{x}\log \csc (\frac{5\pi}{6})^{}=\log (\sqrt[]{2}) \\ x\log (2)=\text{ log(}\sqrt[]{2}) \\ x=\frac{\log\sqrt[]{2}}{\log\text{ 2}} \\ x=\frac{1}{2} \end{gathered}[/tex]

• Notice that we've descended that exponent x, to become a factor (3rd line).

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• Then divided both log with a common base, in this case, base 10.

3) Hence that equation yields 1/2 as its result.

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