Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)-1=0
- Equation 64-x^2=0
-
Equation sin(5*x)=-1
-
Equation 7^x-2=49
- Express {x} in terms of y where:
- -6*x-2*y=15
- -5*x-19*y=-4
- -8*x-11*y=19
- -7*x+16*y=12
- Sum of series:
-
49
- Integral of d{x}:
-
49
- Derivative of:
-
49
-
Identical expressions
- seven ^x- two = forty-nine
- 7 to the power of x minus 2 equally 49
- seven to the power of x minus two equally forty minus nine
- 7x-2=49
-
Similar expressions
- 7^x+2=49
7^x-2=49 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$7^{x} - 2 = 49$$
or
$$\left(7^{x} - 2\right) - 49 = 0$$
or
$$7^{x} = 51$$
or
$$7^{x} = 51$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 51 = 0$$
or
$$v - 51 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 51$$
We get the answer: v = 51
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(51 \right)}}{\log{\left(7 \right)}} = \frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
$$7^{x} - 2 = 49$$
or
$$\left(7^{x} - 2\right) - 49 = 0$$
or
$$7^{x} = 51$$
or
$$7^{x} = 51$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 51 = 0$$
or
$$v - 51 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 51$$
We get the answer: v = 51
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(51 \right)}}{\log{\left(7 \right)}} = \frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
Sum and product of roots
[src]
sum
log(51) ------- log(7)
$$\frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
=
log(51) ------- log(7)
$$\frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
product
log(51) ------- log(7)
$$\frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
=
log(51) ------- log(7)
$$\frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
log(51)/log(7)
Rapid solution
[src]
log(51)
x1 = -------
log(7)
$$x_{1} = \frac{\log{\left(51 \right)}}{\log{\left(7 \right)}}$$
x1 = log(51)/log(7)
The graph