Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3*x^2-8*x-3=0
-
Equation x^3=9
- Equation 4/3*x^2-48=0
-
Equation z^4+z^2+1=0
- Express {x} in terms of y where:
- 19*x-3*y=-12
- 14*x+14*y=13
- -10*x+5*y=10
- -18*x+16*y=4
- Sum of series:
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25
- Integral of d{x}:
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25
- Canonical form:
- 25
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Identical expressions
- five ^x- two = twenty-five
- 5 to the power of x minus 2 equally 25
- five to the power of x minus two equally twenty minus five
- 5x-2=25
-
Similar expressions
- 5^x+2=25
5^x-2=25 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$5^{x} - 2 = 25$$
or
$$\left(5^{x} - 2\right) - 25 = 0$$
or
$$5^{x} = 27$$
or
$$5^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(5 \right)}} = \frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
$$5^{x} - 2 = 25$$
or
$$\left(5^{x} - 2\right) - 25 = 0$$
or
$$5^{x} = 27$$
or
$$5^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(5 \right)}} = \frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
Sum and product of roots
[src]
sum
3*log(3) -------- log(5)
$$\frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
=
3*log(3) -------- log(5)
$$\frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
product
3*log(3) -------- log(5)
$$\frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
=
3*log(3) -------- log(5)
$$\frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
3*log(3)/log(5)
Rapid solution
[src]
3*log(3)
x1 = --------
log(5)
$$x_{1} = \frac{3 \log{\left(3 \right)}}{\log{\left(5 \right)}}$$
x1 = 3*log(3)/log(5)
The graph