Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+3)^2=4
-
Equation 2*x^2-18=0
-
Equation 3*x-7/8-x-3/6=1
- Equation (-5*x+3)*(-x+8)=0
- Express {x} in terms of y where:
- -10*x+8*y=2
- 13*x+3*y=6
- 7*x-18*y=-4
- -2*x+13*y=-6
- Derivative of:
-
3^x
- 30
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
- Sum of series:
-
30
- 30
-
Identical expressions
- three ^x= thirty
- 3 to the power of x equally 30
- three to the power of x equally thirty
- 3x=30
3^x=30 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 30$$
or
$$3^{x} - 30 = 0$$
or
$$3^{x} = 30$$
or
$$3^{x} = 30$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 30 = 0$$
or
$$v - 30 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 30$$
We get the answer: v = 30
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(30 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
$$3^{x} = 30$$
or
$$3^{x} - 30 = 0$$
or
$$3^{x} = 30$$
or
$$3^{x} = 30$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 30 = 0$$
or
$$v - 30 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 30$$
We get the answer: v = 30
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(30 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
Sum and product of roots
[src]
sum
log(30) ------- log(3)
$$\frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
=
log(30) ------- log(3)
$$\frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
product
log(30) ------- log(3)
$$\frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
=
log(30) ------- log(3)
$$\frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
log(30)/log(3)
Rapid solution
[src]
log(30)
x1 = -------
log(3)
$$x_{1} = \frac{\log{\left(30 \right)}}{\log{\left(3 \right)}}$$
x1 = log(30)/log(3)
The graph