Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-11)/(x-6)=11/16
-
Equation x^2-4x+6=0
-
Equation 5*x=12
-
Equation 2*sin(x)*cos(x)=0
- Express {x} in terms of y where:
- -20*x-7*y=-17
- -16*x-9*y=-5
- -8*x-11*y=1
- -7*x-16*y=8
- Derivative of:
- e^x-4
-
Identical expressions
- e^x- four = zero
- e to the power of x minus 4 equally 0
- e to the power of x minus four equally zero
- ex-4=0
- e^x-4=O
-
Similar expressions
- e^x+4=0
e^x-4=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$e^{x} - 4 = 0$$
or
$$e^{x} - 4 = 0$$
or
$$e^{x} = 4$$
or
$$e^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 4 = 0$$
or
$$v - 4 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 4$$
We get the answer: v = 4
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(e \right)}} = \log{\left(4 \right)}$$
$$e^{x} - 4 = 0$$
or
$$e^{x} - 4 = 0$$
or
$$e^{x} = 4$$
or
$$e^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 4 = 0$$
or
$$v - 4 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 4$$
We get the answer: v = 4
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(e \right)}} = \log{\left(4 \right)}$$
Sum and product of roots
[src]
sum
log(4)
$$\log{\left(4 \right)}$$
=
log(4)
$$\log{\left(4 \right)}$$
product
log(4)
$$\log{\left(4 \right)}$$
=
log(4)
$$\log{\left(4 \right)}$$
log(4)
The graph