Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-x-7=0
-
Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
-
Equation e^x=4
-
Equation x^3=x^2-7x+7
- Express {x} in terms of y where:
- -6*x-13*y=17
- -7*x+5*y=1
- -6*x-19*y=7
- -19*x-4*y=-19
- Derivative of:
-
5^x
- Integral of d{x}:
-
5^x
- Graphing y =:
-
5^x
-
Identical expressions
- five ^x= three
- 5 to the power of x equally 3
- five to the power of x equally three
- 5x=3
5^x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$5^{x} = 3$$
or
$$5^{x} - 3 = 0$$
or
$$5^{x} = 3$$
or
$$5^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 3 = 0$$
or
$$v - 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 3$$
We get the answer: v = 3
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
$$5^{x} = 3$$
or
$$5^{x} - 3 = 0$$
or
$$5^{x} = 3$$
or
$$5^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 3 = 0$$
or
$$v - 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 3$$
We get the answer: v = 3
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
Sum and product of roots
[src]
sum
log(3) ------ log(5)
$$\frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
=
log(3) ------ log(5)
$$\frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
product
log(3) ------ log(5)
$$\frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
=
log(3) ------ log(5)
$$\frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
log(3)/log(5)
Rapid solution
[src]
log(3)
x1 = ------
log(5)
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}}$$
x1 = log(3)/log(5)
The graph