Mister Exam
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How to use it?
- Equation:
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Equation x^2-5x-14=0
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Identical expressions
- two =log2(one /(eight /n))
- 2 equally logarithm of 2(1 divide by (8 divide by n))
- two equally logarithm of 2(one divide by (eight divide by n))
- 2=log21/8/n
- 2=log2(1 divide by (8 divide by n))
2=log2(1/(8/n)) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
/ 1 \
log|---|
|/8\|
||-||
\\n//
2 = --------
log(2)
$$2 = \frac{\log{\left(\frac{1}{8 \frac{1}{n}} \right)}}{\log{\left(2 \right)}}$$
Detail solution
Given the equation
$$2 = \frac{\log{\left(\frac{1}{8 \frac{1}{n}} \right)}}{\log{\left(2 \right)}}$$
Transfer the right side of the equation left part with negative sign
$$- \frac{\log{\left(\frac{n}{8} \right)}}{\log{\left(2 \right)}} = -2$$
Let's divide both parts of the equation by the multiplier of log =-1/log(2)
$$\log{\left(\frac{n}{8} \right)} = 2 \log{\left(2 \right)}$$
This equation is of the form:
By definition log
then
$$\frac{n}{8} = e^{- \frac{2}{\left(-1\right) \frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$\frac{n}{8} = 4$$
$$n = 32$$
$$2 = \frac{\log{\left(\frac{1}{8 \frac{1}{n}} \right)}}{\log{\left(2 \right)}}$$
Transfer the right side of the equation left part with negative sign
$$- \frac{\log{\left(\frac{n}{8} \right)}}{\log{\left(2 \right)}} = -2$$
Let's divide both parts of the equation by the multiplier of log =-1/log(2)
$$\log{\left(\frac{n}{8} \right)} = 2 \log{\left(2 \right)}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$\frac{n}{8} = e^{- \frac{2}{\left(-1\right) \frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$\frac{n}{8} = 4$$
$$n = 32$$