Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-4x+6=0
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Equation cos(4*x)=0
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Equation x^2-21=4x
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Equation 5x-9=3x+1
- Express {x} in terms of y where:
- -12*x+17*y=-11
- -11*x-9*y=-17
- -8*x-16*y=18
- -10*x-19*y=3
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Identical expressions
- log4*(five +x)= two
- logarithm of 4 multiply by (5 plus x) equally 2
- logarithm of 4 multiply by (five plus x) equally two
- log4(5+x)=2
- log45+x=2
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Similar expressions
- log4*(5-x)=2
log4*(5+x)=2 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:
$$2 x \log{\left(2 \right)} + 10 \log{\left(2 \right)} = 2$$
Divide both parts of the equation by (10*log(2) + 2*x*log(2))/x
We get the answer: x = (1 - log(32))/log(2)
log(4)*(5+x) = 2
Expand expressions:
10*log(2) + 2*x*log(2) = 2
Reducing, you get:
-2 + 10*log(2) + 2*x*log(2) = 0
Expand brackets in the left part
-2 + 10*log2 + 2*x*log2 = 0
Move free summands (without x)
from left part to right part, we given:
$$2 x \log{\left(2 \right)} + 10 \log{\left(2 \right)} = 2$$
Divide both parts of the equation by (10*log(2) + 2*x*log(2))/x
x = 2 / ((10*log(2) + 2*x*log(2))/x)
We get the answer: x = (1 - log(32))/log(2)
Sum and product of roots
[src]
sum
2 - log(1024)
-------------
log(4)
$$\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}}$$
=
2 - log(1024)
-------------
log(4)
$$\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}}$$
product
2 - log(1024)
-------------
log(4)
$$\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}}$$
=
2 - log(1024)
-------------
log(4)
$$\frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}}$$
(2 - log(1024))/log(4)
Rapid solution
[src]
2 - log(1024)
x1 = -------------
log(4)
$$x_{1} = \frac{2 - \log{\left(1024 \right)}}{\log{\left(4 \right)}}$$
x1 = (2 - log(1024))/log(4)