Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 25*x^3-10*x^2+x=0
-
Equation 2x^2-x-1=x^2-5x-(-1-x^2)
-
Equation 2^x=5
-
Equation (x-10)^2=(x+4)^2
- Express {x} in terms of y where:
- 15*x+12*y=-19
- -19*x-20*y=-4
- -18*x+12*y=-8
- -14*x+4*y=-16
- Derivative of:
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2^x
- Integral of d{x}:
-
2^x
- Graphing y =:
- 2^x
-
Identical expressions
- two ^x= five
- 2 to the power of x equally 5
- two to the power of x equally five
- 2x=5
-
Similar expressions
- 8/4^x-6*2^x+1=0
2^x=5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = 5$$
or
$$2^{x} - 5 = 0$$
or
$$2^{x} = 5$$
or
$$2^{x} = 5$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 5 = 0$$
or
$$v - 5 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 5$$
We get the answer: v = 5
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
$$2^{x} = 5$$
or
$$2^{x} - 5 = 0$$
or
$$2^{x} = 5$$
or
$$2^{x} = 5$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 5 = 0$$
or
$$v - 5 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 5$$
We get the answer: v = 5
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
log(5) ------ log(2)
$$\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
=
log(5) ------ log(2)
$$\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
product
log(5) ------ log(2)
$$\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
=
log(5) ------ log(2)
$$\frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
log(5)/log(2)
Rapid solution
[src]
log(5)
x1 = ------
log(2)
$$x_{1} = \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
x1 = log(5)/log(2)
The graph