Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x+y=15
-
Equation (x-11)/(x-6)=11/16
-
Equation -(-y+4)+2*y+1=0
-
Equation 7(x+2)=-14
- Express {x} in terms of y where:
- -5*x+19*y=-12
- 4*x+7*y=-9
- 20*x+16*y=-7
- -4*x+19*y=-3
- Integral of d{x}:
-
1/x^5
- Derivative of:
-
1/x^5
- Graphing y =:
- 1/x^5
- Limit of the function:
- x^z
-
Identical expressions
- one /x^ five =x^z
- 1 divide by x to the power of 5 equally x to the power of z
- one divide by x to the power of five equally x to the power of z
- 1/x5=xz
- 1/x⁵=x^z
- 1 divide by x^5=x^z
1/x^5=x^z equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{1}{x^{5}} = x^{z}$$
or
$$- x^{z} + \frac{1}{x^{5}} = 0$$
or
$$- x^{z} = - \frac{1}{x^{5}}$$
or
$$x^{z} = \frac{1}{x^{5}}$$
- this is the simplest exponential equation
Do replacement
$$v = x^{z}$$
we get
$$v - \frac{1}{x^{5}} = 0$$
or
$$v - \frac{1}{x^{5}} = 0$$
do backward replacement
$$x^{z} = v$$
or
$$z = \frac{\log{\left(v \right)}}{\log{\left(x \right)}}$$
The final answer
$$z_{1} = \frac{\log{\left(\frac{1}{x^{5}} \right)}}{\log{\left(x \right)}} = \frac{\log{\left(\frac{1}{x^{5}} \right)}}{\log{\left(x \right)}}$$
$$\frac{1}{x^{5}} = x^{z}$$
or
$$- x^{z} + \frac{1}{x^{5}} = 0$$
or
$$- x^{z} = - \frac{1}{x^{5}}$$
or
$$x^{z} = \frac{1}{x^{5}}$$
- this is the simplest exponential equation
Do replacement
$$v = x^{z}$$
we get
$$v - \frac{1}{x^{5}} = 0$$
or
$$v - \frac{1}{x^{5}} = 0$$
do backward replacement
$$x^{z} = v$$
or
$$z = \frac{\log{\left(v \right)}}{\log{\left(x \right)}}$$
The final answer
$$z_{1} = \frac{\log{\left(\frac{1}{x^{5}} \right)}}{\log{\left(x \right)}} = \frac{\log{\left(\frac{1}{x^{5}} \right)}}{\log{\left(x \right)}}$$
The graph