Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x+12=5
-
Equation x^3=4
-
Equation 0,144:(3,4-x)=2,4
-
Equation x^4=(x-56)^2
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 18*x+20*y=-2
- -5*x-6*y=-1
- -17*x-15*y=-17
- Derivative of:
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4^x
- Integral of d{x}:
-
4^x
- Graphing y =:
- 4^x
-
Identical expressions
- four ^x= eight
- 4 to the power of x equally 8
- four to the power of x equally eight
- 4x=8
-
Similar expressions
- (1/4)^x-4=1/64
4^x=8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$4^{x} = 8$$
or
$$4^{x} - 8 = 0$$
or
$$4^{x} = 8$$
or
$$4^{x} = 8$$
- this is the simplest exponential equation
Do replacement
$$v = 4^{x}$$
we get
$$v - 8 = 0$$
or
$$v - 8 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 8$$
We get the answer: v = 8
do backward replacement
$$4^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(4 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(8 \right)}}{\log{\left(4 \right)}} = \frac{3}{2}$$
$$4^{x} = 8$$
or
$$4^{x} - 8 = 0$$
or
$$4^{x} = 8$$
or
$$4^{x} = 8$$
- this is the simplest exponential equation
Do replacement
$$v = 4^{x}$$
we get
$$v - 8 = 0$$
or
$$v - 8 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 8$$
We get the answer: v = 8
do backward replacement
$$4^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(4 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(8 \right)}}{\log{\left(4 \right)}} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
3 log(8) pi*I - + -------- + ------ 2 2*log(2) log(2)
$$\frac{3}{2} + \left(\frac{\log{\left(8 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right)$$
=
3 log(8) pi*I - + -------- + ------ 2 2*log(2) log(2)
$$\frac{\log{\left(8 \right)}}{2 \log{\left(2 \right)}} + \frac{3}{2} + \frac{i \pi}{\log{\left(2 \right)}}$$
product
/ log(8) pi*I \
3*|-------- + ------|
\2*log(2) log(2)/
---------------------
2
$$\frac{3 \left(\frac{\log{\left(8 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}\right)}{2}$$
=
9 3*pi*I - + -------- 4 2*log(2)
$$\frac{9}{4} + \frac{3 i \pi}{2 \log{\left(2 \right)}}$$
9/4 + 3*pi*i/(2*log(2))
Rapid solution
[src]
x1 = 3/2
$$x_{1} = \frac{3}{2}$$
log(8) pi*I
x2 = -------- + ------
2*log(2) log(2)
$$x_{2} = \frac{\log{\left(8 \right)}}{2 \log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$
x2 = log(8)/(2*log(2)) + i*pi/log(2)
The graph