Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x=3,5
-
Equation x-log(x^2+1)=0
-
Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
-
Equation -x^2+7*x+8=0
- Express {x} in terms of y where:
- 2*x-9*y=-10
- 13*x-12*y=0
- 20*x+2*y=-1
- 11*x+19*y=-4
- Integral of d{x}:
- 4^(x-1)
-
Identical expressions
- four ^(x- one)= one
- 4 to the power of (x minus 1) equally 1
- four to the power of (x minus one) equally one
- 4(x-1)=1
- 4x-1=1
- 4^x-1=1
-
Similar expressions
- 4^(x+1)=1
4^(x-1)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$4^{x - 1} = 1$$
or
$$4^{x - 1} - 1 = 0$$
or
$$\frac{4^{x}}{4} = 1$$
or
$$4^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = 4^{x}$$
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
$$4^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(4 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(4 \right)}} = 1$$
$$4^{x - 1} = 1$$
or
$$4^{x - 1} - 1 = 0$$
or
$$\frac{4^{x}}{4} = 1$$
or
$$4^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = 4^{x}$$
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
$$4^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(4 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(4 \right)}} = 1$$
Rapid solution
[src]
x1 = 1
$$x_{1} = 1$$
pi*I
x2 = 1 + ------
log(2)
$$x_{2} = 1 + \frac{i \pi}{\log{\left(2 \right)}}$$
x2 = 1 + i*pi/log(2)
Sum and product of roots
[src]
sum
pi*I
1 + 1 + ------
log(2)
$$1 + \left(1 + \frac{i \pi}{\log{\left(2 \right)}}\right)$$
=
pi*I
2 + ------
log(2)
$$2 + \frac{i \pi}{\log{\left(2 \right)}}$$
product
pi*I
1 + ------
log(2)
$$1 + \frac{i \pi}{\log{\left(2 \right)}}$$
=
pi*I
1 + ------
log(2)
$$1 + \frac{i \pi}{\log{\left(2 \right)}}$$
1 + pi*i/log(2)
The graph