Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+5*x-14=0
-
Equation x²-4x+3=0
-
Equation x=x^9
-
Equation 6x=x-2
- Express {x} in terms of y where:
- 16*x+5*y=-14
- -16*x-13*y=-1
- 12*x-2*y=-18
- -7*x+8*y=18
- Graphing y =:
- 6^x+5
- Sum of series:
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36
- The double integral of:
- 36
- 36
-
Identical expressions
- six ^x+ five = thirty-six
- 6 to the power of x plus 5 equally 36
- six to the power of x plus five equally thirty minus six
- 6x+5=36
-
Similar expressions
- 6^x-5=36
6^x+5=36 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$6^{x} + 5 = 36$$
or
$$\left(6^{x} + 5\right) - 36 = 0$$
or
$$6^{x} = 31$$
or
$$6^{x} = 31$$
- this is the simplest exponential equation
Do replacement
$$v = 6^{x}$$
we get
$$v - 31 = 0$$
or
$$v - 31 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 31$$
We get the answer: v = 31
do backward replacement
$$6^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(6 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
$$6^{x} + 5 = 36$$
or
$$\left(6^{x} + 5\right) - 36 = 0$$
or
$$6^{x} = 31$$
or
$$6^{x} = 31$$
- this is the simplest exponential equation
Do replacement
$$v = 6^{x}$$
we get
$$v - 31 = 0$$
or
$$v - 31 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 31$$
We get the answer: v = 31
do backward replacement
$$6^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(6 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
Sum and product of roots
[src]
sum
log(31) ------- log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
=
log(31) ------- log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
product
log(31) ------- log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
=
log(31) ------- log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
log(31)/log(6)
Rapid solution
[src]
log(31)
x1 = -------
log(6)
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
x1 = log(31)/log(6)
The graph