Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -20*(x-13)=-220
-
Equation x-x/12=55/12
-
Equation 3^x=81
-
Equation 12-x^2=11
- Express {x} in terms of y where:
- 18*x+19*y=7
- -10*x+13*y=5
- 16*x-15*y=4
- 1*x+6*y=6
- Derivative of:
-
3^x
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
- Sum of series:
-
81
-
Identical expressions
- three ^x= eighty-one
- 3 to the power of x equally 81
- three to the power of x equally eighty minus one
- 3x=81
-
Similar expressions
- 9^x-7*3^x-18=0
- 3^x=243
- (79*exp(28*10^((-3)*x)))/25=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 9^x+3*3^x-18=0
3^x=81 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 81$$
or
$$3^{x} - 81 = 0$$
or
$$3^{x} = 81$$
or
$$3^{x} = 81$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 81 = 0$$
or
$$v - 81 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 81$$
We get the answer: v = 81
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(81 \right)}}{\log{\left(3 \right)}} = 4$$
$$3^{x} = 81$$
or
$$3^{x} - 81 = 0$$
or
$$3^{x} = 81$$
or
$$3^{x} = 81$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 81 = 0$$
or
$$v - 81 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 81$$
We get the answer: v = 81
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(81 \right)}}{\log{\left(3 \right)}} = 4$$
The graph