Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2-8x=0
- Equation (3*x*x*(x^4-6*x*x+10)-x^3*(4*x^3-12*x))/(x^4-6*x^2+10)^2=0=0
- Equation (y-2)(y+3)-(y-2)×(y-2)
- Equation 7^(x-2)=6
- Express {x} in terms of y where:
- -6*x-12*y=-3
- 19*x+8*y=15
- -7*x-1*y=1
- 5*x+2*y=13
-
Identical expressions
- seven ^(x- two)= six
- 7 to the power of (x minus 2) equally 6
- seven to the power of (x minus two) equally six
- 7(x-2)=6
- 7x-2=6
- 7^x-2=6
-
Similar expressions
- 7^(x+2)=6
7^(x-2)=6 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$7^{x - 2} = 6$$
or
$$7^{x - 2} - 6 = 0$$
or
$$\frac{7^{x}}{49} = 6$$
or
$$7^{x} = 294$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 294 = 0$$
or
$$v - 294 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 294$$
We get the answer: v = 294
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(294 \right)}}{\log{\left(7 \right)}} = \frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
$$7^{x - 2} = 6$$
or
$$7^{x - 2} - 6 = 0$$
or
$$\frac{7^{x}}{49} = 6$$
or
$$7^{x} = 294$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 294 = 0$$
or
$$v - 294 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 294$$
We get the answer: v = 294
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(294 \right)}}{\log{\left(7 \right)}} = \frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
Sum and product of roots
[src]
sum
log(294) -------- log(7)
$$\frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
=
log(294) -------- log(7)
$$\frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
product
log(294) -------- log(7)
$$\frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
=
log(294) -------- log(7)
$$\frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
log(294)/log(7)
Rapid solution
[src]
log(294)
x1 = --------
log(7)
$$x_{1} = \frac{\log{\left(294 \right)}}{\log{\left(7 \right)}}$$
x1 = log(294)/log(7)