Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x+9=13-x
-
Equation x^2+4x+13=0
-
Equation 3^x=8
-
Equation -3x+1+(x-5)=5(3-x)+5
- Express {x} in terms of y where:
- 9*x-19*y=-20
- 2*x+13*y=-7
- -7*x-1*y=7
- 9*x-14*y=-6
- Derivative of:
-
3^x
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
-
Identical expressions
- three ^x= eight
- 3 to the power of x equally 8
- three to the power of x equally eight
- 3x=8
3^x=8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 8$$
or
$$3^{x} - 8 = 0$$
or
$$3^{x} = 8$$
or
$$3^{x} = 8$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
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
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(8 \right)}}{\log{\left(3 \right)}} = \frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
$$3^{x} = 8$$
or
$$3^{x} - 8 = 0$$
or
$$3^{x} = 8$$
or
$$3^{x} = 8$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
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
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(8 \right)}}{\log{\left(3 \right)}} = \frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
Sum and product of roots
[src]
sum
3*log(2) -------- log(3)
$$\frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
=
3*log(2) -------- log(3)
$$\frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
product
3*log(2) -------- log(3)
$$\frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
=
3*log(2) -------- log(3)
$$\frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
3*log(2)/log(3)
Rapid solution
[src]
3*log(2)
x1 = --------
log(3)
$$x_{1} = \frac{3 \log{\left(2 \right)}}{\log{\left(3 \right)}}$$
x1 = 3*log(2)/log(3)
The graph