MD06CE: Logs and Exponentials

October 24, 2016 Mouctar Uncategorized 0

MD06CE: Logs and Exponentials

The following execises will be used to practice solving problems related to logarithms and exponential functions. These are hands-on and may be solved through our videos.

Solve for $x$

$\ln (\sin x)+\ln (\cos x)=\ln \sqrt{3}-\ln 4$

Solution:

$\ln (\sin x)+\ln (\cos x)=\ln \sqrt{3}-\ln 4$

$\ln (\sin x \cos x)=\ln \frac{\sqrt{3}}{4}$

$\sin x \cos x=\frac{\sqrt{3}}{4}$

$2\sin x \cos x=\frac{\sqrt{3}}{2}$

$\sin 2x=\frac{\sqrt{3}}{2}$

If we look at the unit circle, we can see that we have an angle in the first quadrant and another at the second quadrant.

$2x=\frac{\pi}{3}$

$x=\frac{\pi}{6}+ 2k_1\pi$

Another angle supplementary to this one will have the same results.

$2x=\pi-\frac{\pi}{3}$

$2x=\frac{2\pi}{3}$

$x=\frac{\pi}{3}+ 2k_2\pi$

Finally:

Answer: $x=\frac{\pi}{3}+ 2k_1\pi$ and $x=\frac{\pi}{6}+ 2k_2\pi$

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MD06CE: Logs and Exponentials

MD06CE: Logs and Exponentials

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