Mister Exam
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- Equation:
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Equation 5-x=4(x-3)
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Equation exp(x)=0
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Equation 3^x=8
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Identical expressions
- log^3x+4log^3x= nine
- logarithm of cubed x plus 4 logarithm of cubed x equally 9
- logarithm of cubed x plus 4 logarithm of cubed x equally nine
- log3x+4log3x=9
- log³x+4log³x=9
- log to the power of 3x+4log to the power of 3x=9
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Similar expressions
- log^3x-4log^3x=9
log^3x+4log^3x=9 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3 3 log (x) + 4*log (x) = 9
$$\log{\left(x \right)}^{3} + 4 \log{\left(x \right)}^{3} = 9$$
Rapid solution
[src]
2/3
15
-----
5
x1 = e
$$x_{1} = e^{\frac{15^{\frac{2}{3}}}{5}}$$
2/3 2/3
-15 -15
/ 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\
|3*\/ 3 *5 | 10 10 |3*\/ 3 *5 |
x2 = cos|------------|*e - I*e *sin|------------|
\ 10 / \ 10 /
$$x_{2} = \frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}$$
2/3 2/3
-15 -15
/ 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\
|3*\/ 3 *5 | 10 10 |3*\/ 3 *5 |
x3 = cos|------------|*e + I*e *sin|------------|
\ 10 / \ 10 /
$$x_{3} = \frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}$$
x3 = exp(-15^(2/3)/10)*cos(3*3^(1/6)*5^(2/3)/10) + i*exp(-15^(2/3)/10)*sin(3*3^(1/6)*5^(2/3)/10)
Sum and product of roots
[src]
sum
2/3 2/3 2/3 2/3 2/3
15 -15 -15 -15 -15
----- / 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\ / 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\
5 |3*\/ 3 *5 | 10 10 |3*\/ 3 *5 | |3*\/ 3 *5 | 10 10 |3*\/ 3 *5 |
e + cos|------------|*e - I*e *sin|------------| + cos|------------|*e + I*e *sin|------------|
\ 10 / \ 10 / \ 10 / \ 10 /
$$\left(e^{\frac{15^{\frac{2}{3}}}{5}} + \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right)\right) + \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right)$$
=
2/3 2/3
-15 15
/ 6 ___ 2/3\ ------- -----
|3*\/ 3 *5 | 10 5
2*cos|------------|*e + e
\ 10 /
$$\frac{2 \cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + e^{\frac{15^{\frac{2}{3}}}{5}}$$
product
2/3 / 2/3 2/3 \ / 2/3 2/3 \
15 | -15 -15 | | -15 -15 |
----- | / 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\| | / 6 ___ 2/3\ ------- ------- / 6 ___ 2/3\|
5 | |3*\/ 3 *5 | 10 10 |3*\/ 3 *5 || | |3*\/ 3 *5 | 10 10 |3*\/ 3 *5 ||
e *|cos|------------|*e - I*e *sin|------------||*|cos|------------|*e + I*e *sin|------------||
\ \ 10 / \ 10 // \ \ 10 / \ 10 //
$$\left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} - \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right) e^{\frac{15^{\frac{2}{3}}}{5}} \left(\frac{\cos{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}} + \frac{i \sin{\left(\frac{3 \sqrt[6]{3} \cdot 5^{\frac{2}{3}}}{10} \right)}}{e^{\frac{15^{\frac{2}{3}}}{10}}}\right)$$
=
1
$$1$$
1
Numerical answer
[src]
x1 = 3.37515213084549
x2 = 0.269198074615172 - 0.473091257293331*i
x3 = 0.269198074615172 + 0.473091257293331*i
x3 = 0.269198074615172 + 0.473091257293331*i