Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x+970=69*32
- Equation x^4-50*x^2+49=0
-
Equation (x^2-4)^2+(x^2-3x-10)^2=0
-
Equation 3^x=7
- Express {x} in terms of y where:
- 1*x+6*y=-6
- -5*x+6*y=-8
- -2*x-9*y=10
- 11*x-12*y=11
- Derivative of:
-
3^x
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
-
Identical expressions
- three ^x= seven
- 3 to the power of x equally 7
- three to the power of x equally seven
- 3x=7
-
Similar expressions
- 9^x-7*3^x-18=0
- 9^x+3*3^x-18=0
- 3^x=243
- -3^(x+2)+9^x+14=0
3^x=7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 7$$
or
$$3^{x} - 7 = 0$$
or
$$3^{x} = 7$$
or
$$3^{x} = 7$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 7 = 0$$
or
$$v - 7 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 7$$
We get the answer: v = 7
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
$$3^{x} = 7$$
or
$$3^{x} - 7 = 0$$
or
$$3^{x} = 7$$
or
$$3^{x} = 7$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 7 = 0$$
or
$$v - 7 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 7$$
We get the answer: v = 7
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
Rapid solution
[src]
log(7)
x1 = ------
log(3)
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
x1 = log(7)/log(3)
Sum and product of roots
[src]
sum
log(7) ------ log(3)
$$\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
=
log(7) ------ log(3)
$$\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
product
log(7) ------ log(3)
$$\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
=
log(7) ------ log(3)
$$\frac{\log{\left(7 \right)}}{\log{\left(3 \right)}}$$
log(7)/log(3)
The graph