Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4,3x-3,5=2,5x+1,9
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Equation x^6=-64
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Equation sin(x)=5/2
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Equation (x+4)(x+2)-(x-0,5)(x+2)=0
- Express {x} in terms of y where:
- -8*x+5*y=-17
- -18*x-17*y=-5
- -13*x+5*y=15
- 13*x-7*y=8
- Sum of series:
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1/5
- Integral of d{x}:
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1/5
- Limit of the function:
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1/5
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Identical expressions
- √(five)^(x- one)= one / five
- √(5) to the power of (x minus 1) equally 1 divide by 5
- √(five) to the power of (x minus one) equally one divide by five
- √(5)(x-1)=1/5
- √5x-1=1/5
- √5^x-1=1/5
- √(5)^(x-1)=1 divide by 5
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Similar expressions
- √(5)^(x+1)=1/5
- 2*((|x|)+3)/3=13*((|x|)-1)/5
√(5)^(x-1)=1/5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\left(\sqrt{5}\right)^{x - 1} = \frac{1}{5}$$
or
$$\left(\sqrt{5}\right)^{x - 1} - \frac{1}{5} = 0$$
or
$$\frac{\sqrt{5} \cdot 5^{\frac{x}{2}}}{5} = \frac{1}{5}$$
or
$$5^{\frac{x}{2}} = \frac{\sqrt{5}}{5}$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{\frac{x}{2}}$$
we get
$$v - \frac{\sqrt{5}}{5} = 0$$
or
$$v - \frac{\sqrt{5}}{5} = 0$$
Expand brackets in the left part
Divide both parts of the equation by (v - sqrt(5)/5)/v
We get the answer: v = sqrt(5)/5
do backward replacement
$$5^{\frac{x}{2}} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(\sqrt{5} \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(\frac{\sqrt{5}}{5} \right)}}{\log{\left(\sqrt{5} \right)}} = -1$$
$$\left(\sqrt{5}\right)^{x - 1} = \frac{1}{5}$$
or
$$\left(\sqrt{5}\right)^{x - 1} - \frac{1}{5} = 0$$
or
$$\frac{\sqrt{5} \cdot 5^{\frac{x}{2}}}{5} = \frac{1}{5}$$
or
$$5^{\frac{x}{2}} = \frac{\sqrt{5}}{5}$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{\frac{x}{2}}$$
we get
$$v - \frac{\sqrt{5}}{5} = 0$$
or
$$v - \frac{\sqrt{5}}{5} = 0$$
Expand brackets in the left part
v - sqrt5/5 = 0
Divide both parts of the equation by (v - sqrt(5)/5)/v
v = 0 / ((v - sqrt(5)/5)/v)
We get the answer: v = sqrt(5)/5
do backward replacement
$$5^{\frac{x}{2}} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(\sqrt{5} \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(\frac{\sqrt{5}}{5} \right)}}{\log{\left(\sqrt{5} \right)}} = -1$$