Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=8
-
Equation 11-5(2x+1)=41-9x
-
Equation 6(x-3)+2(x+2)=1
-
Equation 3^x-3=81
- Express {x} in terms of y where:
- 8*x+2*y=4
- 7*x+5*y=15
- -15*x-7*y=-12
- 8*x-6*y=-18
- Graphing y =:
- 3^x-3
- Sum of series:
-
81
-
Identical expressions
- three ^x- three = eighty-one
- 3 to the power of x minus 3 equally 81
- three to the power of x minus three equally eighty minus one
- 3x-3=81
-
Similar expressions
- 3^x+3=81
3^x-3=81 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} - 3 = 81$$
or
$$\left(3^{x} - 3\right) - 81 = 0$$
or
$$3^{x} = 84$$
or
$$3^{x} = 84$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 84 = 0$$
or
$$v - 84 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 84$$
We get the answer: v = 84
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
$$3^{x} - 3 = 81$$
or
$$\left(3^{x} - 3\right) - 81 = 0$$
or
$$3^{x} = 84$$
or
$$3^{x} = 84$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 84 = 0$$
or
$$v - 84 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 84$$
We get the answer: v = 84
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
Rapid solution
[src]
log(84)
x1 = -------
log(3)
$$x_{1} = \frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
x1 = log(84)/log(3)
Sum and product of roots
[src]
sum
log(84) ------- log(3)
$$\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
=
log(84) ------- log(3)
$$\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
product
log(84) ------- log(3)
$$\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
=
log(84) ------- log(3)
$$\frac{\log{\left(84 \right)}}{\log{\left(3 \right)}}$$
log(84)/log(3)
The graph