Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation 3x-2=0
- Express {x} in terms of y where:
- -9*x+1*y=3
- 5*x+12*y=18
- 18*x+20*y=-2
- 15*x+7*y=2
- Sum of series:
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36
- The double integral of:
- 36
- 36
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Identical expressions
- six ^x- five = thirty-six
- 6 to the power of x minus 5 equally 36
- six to the power of x minus five equally thirty minus six
- 6x-5=36
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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
$$6^{x} = 41$$
or
$$6^{x} = 41$$
- this is the simplest exponential equation
Do replacement
$$v = 6^{x}$$
we get
$$v - 41 = 0$$
or
$$v - 41 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 41$$
We get the answer: v = 41
do backward replacement
$$6^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(6 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(41 \right)}}{\log{\left(6 \right)}} = \frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
$$6^{x} - 5 = 36$$
or
$$\left(6^{x} - 5\right) - 36 = 0$$
or
$$6^{x} = 41$$
or
$$6^{x} = 41$$
- this is the simplest exponential equation
Do replacement
$$v = 6^{x}$$
we get
$$v - 41 = 0$$
or
$$v - 41 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 41$$
We get the answer: v = 41
do backward replacement
$$6^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(6 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(41 \right)}}{\log{\left(6 \right)}} = \frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
Sum and product of roots
[src]
sum
log(41) ------- log(6)
$$\frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
=
log(41) ------- log(6)
$$\frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
product
log(41) ------- log(6)
$$\frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
=
log(41) ------- log(6)
$$\frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
log(41)/log(6)
Rapid solution
[src]
log(41)
x1 = -------
log(6)
$$x_{1} = \frac{\log{\left(41 \right)}}{\log{\left(6 \right)}}$$
x1 = log(41)/log(6)
The graph