Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 5x^2-20=0
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Equation log5x=4log5(3)–1/3log5(27)
- Equation x^4-17x^2+16=0
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Equation 26x-6=8x-42
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- Graphing y =:
- log5x
- Derivative of:
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log5x
- Sum of series:
- log5x
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Identical expressions
- log5x=4log5(three)– one /3log5(twenty-seven)
- logarithm of 5x equally 4 logarithm of 5(3)–1 divide by 3 logarithm of 5(27)
- logarithm of 5x equally 4 logarithm of 5(three)– one divide by 3 logarithm of 5(twenty minus seven)
- log5x=4log53–1/3log527
- log5x=4log5(3)–1 divide by 3log5(27)
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Similar expressions
- 2*log(5)^2*x+3*log(5)*x-2=0
- log5(x+3)=2
- 2*log(5)^2*x-7*log(5)*x+3=0
- log5(x^3+x)-(log5X)=log510
log5x=4log5(3)–1/3log5(27) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4*log(3) log(27)
log(5*x) = -------- - --------
log(5) 3*log(5)
$$\log{\left(5 x \right)} = - \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
Detail solution
Given the equation
$$\log{\left(5 x \right)} = - \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
$$\log{\left(5 x \right)} = - \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
This equation is of the form:
By definition log
then
$$5 x + 0 = e^{\frac{- \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}}{1}}$$
simplify
$$5 x = \frac{3^{\frac{4}{\log{\left(5 \right)}}}}{27^{\frac{1}{3 \log{\left(5 \right)}}}}$$
$$x = \frac{3^{\frac{4}{\log{\left(5 \right)}}}}{5 \cdot 27^{\frac{1}{3 \log{\left(5 \right)}}}}$$
$$\log{\left(5 x \right)} = - \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
$$\log{\left(5 x \right)} = - \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$5 x + 0 = e^{\frac{- \frac{\log{\left(27 \right)}}{3 \log{\left(5 \right)}} + \frac{4 \log{\left(3 \right)}}{\log{\left(5 \right)}}}{1}}$$
simplify
$$5 x = \frac{3^{\frac{4}{\log{\left(5 \right)}}}}{27^{\frac{1}{3 \log{\left(5 \right)}}}}$$
$$x = \frac{3^{\frac{4}{\log{\left(5 \right)}}}}{5 \cdot 27^{\frac{1}{3 \log{\left(5 \right)}}}}$$
Sum and product of roots
[src]
sum
3 ------ log(5) 3 ------- 5
$$\left(\frac{3^{\frac{3}{\log{\left(5 \right)}}}}{5}\right)$$
=
3 ------ log(5) 3 ------- 5
$$\frac{3^{\frac{3}{\log{\left(5 \right)}}}}{5}$$
product
3 ------ log(5) 3 ------- 5
$$\left(\frac{3^{\frac{3}{\log{\left(5 \right)}}}}{5}\right)$$
=
3 ------ log(5) 3 ------- 5
$$\frac{3^{\frac{3}{\log{\left(5 \right)}}}}{5}$$
Rapid solution
[src]
3
------
log(5)
3
x_1 = -------
5
$$x_{1} = \frac{3^{\frac{3}{\log{\left(5 \right)}}}}{5}$$
The graph