Mister Exam
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How to use it?
- Equation:
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Equation 2^2-x-1=x^2-5*x-(-1-x^2)
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Equation x^2=35
-
Equation 10*(x-9)=7
-
Equation x^2+9=0
- Express {x} in terms of y where:
- 18*x-12*y=-20
- 7*x-2*y=20
- -20*x-14*y=5
- -11*x+1*y=12
-
Identical expressions
- log2(5x+ eight)=log23+ four
- logarithm of 2(5x plus 8) equally logarithm of 23 plus 4
- logarithm of 2(5x plus eight) equally logarithm of 23 plus four
- log25x+8=log23+4
-
Similar expressions
- log2(5x+8)=log23-4
- x*log^2(3)+4*x*log(3)-5=0
- log2(5x-8)=log23+4
log2(5x+8)=log23+4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
log(5*x + 8) ------------ = log(23) + 4 log(2)
$$\frac{\log{\left(5 x + 8 \right)}}{\log{\left(2 \right)}} = \log{\left(23 \right)} + 4$$
Detail solution
Given the equation
$$\frac{\log{\left(5 x + 8 \right)}}{\log{\left(2 \right)}} = \log{\left(23 \right)} + 4$$
$$\frac{\log{\left(5 x + 8 \right)}}{\log{\left(2 \right)}} = \log{\left(23 \right)} + 4$$
Let's divide both parts of the equation by the multiplier of log =1/log(2)
$$\log{\left(5 x + 8 \right)} = \left(\log{\left(23 \right)} + 4\right) \log{\left(2 \right)}$$
This equation is of the form:
By definition log
then
$$5 x + 8 = e^{\frac{\log{\left(23 \right)} + 4}{\frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$5 x + 8 = 2^{\log{\left(23 \right)} + 4}$$
$$5 x = -8 + 2^{\log{\left(23 \right)} + 4}$$
$$x = - \frac{8}{5} + \frac{2^{\log{\left(23 \right)} + 4}}{5}$$
$$\frac{\log{\left(5 x + 8 \right)}}{\log{\left(2 \right)}} = \log{\left(23 \right)} + 4$$
$$\frac{\log{\left(5 x + 8 \right)}}{\log{\left(2 \right)}} = \log{\left(23 \right)} + 4$$
Let's divide both parts of the equation by the multiplier of log =1/log(2)
$$\log{\left(5 x + 8 \right)} = \left(\log{\left(23 \right)} + 4\right) \log{\left(2 \right)}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$5 x + 8 = e^{\frac{\log{\left(23 \right)} + 4}{\frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$5 x + 8 = 2^{\log{\left(23 \right)} + 4}$$
$$5 x = -8 + 2^{\log{\left(23 \right)} + 4}$$
$$x = - \frac{8}{5} + \frac{2^{\log{\left(23 \right)} + 4}}{5}$$
Sum and product of roots
[src]
sum
log(23) 8 16*2 - - + ----------- 5 5
$$- \frac{8}{5} + \frac{16 \cdot 2^{\log{\left(23 \right)}}}{5}$$
=
log(23) 8 16*2 - - + ----------- 5 5
$$- \frac{8}{5} + \frac{16 \cdot 2^{\log{\left(23 \right)}}}{5}$$
product
log(23) 8 16*2 - - + ----------- 5 5
$$- \frac{8}{5} + \frac{16 \cdot 2^{\log{\left(23 \right)}}}{5}$$
=
log(23) 8 16*2 - - + ----------- 5 5
$$- \frac{8}{5} + \frac{16 \cdot 2^{\log{\left(23 \right)}}}{5}$$
-8/5 + 16*2^log(23)/5
Rapid solution
[src]
log(23)
8 16*2
x1 = - - + -----------
5 5
$$x_{1} = - \frac{8}{5} + \frac{16 \cdot 2^{\log{\left(23 \right)}}}{5}$$
x1 = -8/5 + 16*2^log(23)/5