Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-x-5=0
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Equation cos(x)=-3
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Equation x²-6x+5=0
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Equation (5+7*a)*15=-30
- Express {x} in terms of y where:
- -2*x+15*y=9
- -15*x-19*y=-2
- -5*x+15*y=6
- -17*x+7*y=-11
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Identical expressions
- log(seven)(3x- five)= one
- logarithm of (7)(3x minus 5) equally 1
- logarithm of (seven)(3x minus five) equally one
- log73x-5=1
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Similar expressions
- log(7)(3x+5)=1
log(7)(3x-5)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
Expand expressions:
Reducing, you get:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$3 x \log{\left(7 \right)} - 5 \log{\left(7 \right)} = 1$$
Divide both parts of the equation by (-5*log(7) + 3*x*log(7))/x
We get the answer: x = (1 + log(16807))/(3*log(7))
log(7)*(3*x-5) = 1
Expand expressions:
-5*log(7) + 3*x*log(7) = 1
Reducing, you get:
-1 - 5*log(7) + 3*x*log(7) = 0
Expand brackets in the left part
-1 - 5*log7 + 3*x*log7 = 0
Move free summands (without x)
from left part to right part, we given:
$$3 x \log{\left(7 \right)} - 5 \log{\left(7 \right)} = 1$$
Divide both parts of the equation by (-5*log(7) + 3*x*log(7))/x
x = 1 / ((-5*log(7) + 3*x*log(7))/x)
We get the answer: x = (1 + log(16807))/(3*log(7))
Sum and product of roots
[src]
sum
1 + log(16807) -------------- 3*log(7)
$$\frac{1 + \log{\left(16807 \right)}}{3 \log{\left(7 \right)}}$$
=
1 + log(16807) -------------- 3*log(7)
$$\frac{1 + \log{\left(16807 \right)}}{3 \log{\left(7 \right)}}$$
product
1 + log(16807) -------------- 3*log(7)
$$\frac{1 + \log{\left(16807 \right)}}{3 \log{\left(7 \right)}}$$
=
1 + log(16807) -------------- 3*log(7)
$$\frac{1 + \log{\left(16807 \right)}}{3 \log{\left(7 \right)}}$$
(1 + log(16807))/(3*log(7))
Rapid solution
[src]
1 + log(16807)
x1 = --------------
3*log(7)
$$x_{1} = \frac{1 + \log{\left(16807 \right)}}{3 \log{\left(7 \right)}}$$
x1 = (1 + log(16807))/(3*log(7))