Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+11*x+30=0
-
Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
-
Equation (|3*x-9|)-(|x+2|)=7
-
Equation 3(x-1)-6=0
- Express {x} in terms of y where:
- 15*x-2*y=14
- -12*x+12*y=8
- -9*x+16*y=-11
- -6*x-2*y=-16
- Sum of series:
-
27
-
Identical expressions
- (one / three)^x- four = twenty-seven
- (1 divide by 3) to the power of x minus 4 equally 27
- (one divide by three) to the power of x minus four equally twenty minus seven
- (1/3)x-4=27
- 1/3x-4=27
- 1/3^x-4=27
- (1 divide by 3)^x-4=27
-
Similar expressions
- (1/3)^x+4=27
(1/3)^x-4=27 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$-4 + \left(\frac{1}{3}\right)^{x} = 27$$
or
$$\left(-4 + \left(\frac{1}{3}\right)^{x}\right) - 27 = 0$$
or
$$\left(\frac{1}{3}\right)^{x} = 31$$
or
$$\left(\frac{1}{3}\right)^{x} = 31$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{1}{3}\right)^{x}$$
we get
$$v - 31 = 0$$
or
$$v - 31 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 31$$
We get the answer: v = 31
do backward replacement
$$\left(\frac{1}{3}\right)^{x} = v$$
or
$$x = - \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(\frac{1}{3} \right)}} = - \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
$$-4 + \left(\frac{1}{3}\right)^{x} = 27$$
or
$$\left(-4 + \left(\frac{1}{3}\right)^{x}\right) - 27 = 0$$
or
$$\left(\frac{1}{3}\right)^{x} = 31$$
or
$$\left(\frac{1}{3}\right)^{x} = 31$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{1}{3}\right)^{x}$$
we get
$$v - 31 = 0$$
or
$$v - 31 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 31$$
We get the answer: v = 31
do backward replacement
$$\left(\frac{1}{3}\right)^{x} = v$$
or
$$x = - \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(\frac{1}{3} \right)}} = - \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
Sum and product of roots
[src]
sum
-log(31) --------- log(3)
$$- \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
=
-log(31) --------- log(3)
$$- \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
product
-log(31) --------- log(3)
$$- \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
=
-log(31) --------- log(3)
$$- \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
-log(31)/log(3)
Rapid solution
[src]
-log(31)
x1 = ---------
log(3)
$$x_{1} = - \frac{\log{\left(31 \right)}}{\log{\left(3 \right)}}$$
x1 = -log(31)/log(3)