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Tanya [424]
2 years ago
5

Find the exact solution to the equation. 5^(6-2x) = 25

Mathematics
1 answer:
STatiana [176]2 years ago
3 0

Answer:

x = 2

Step-by-step explanation:

Note that 25 = 5² , then

5^{(6-2x)} = 5²

Since the bases on both sides are 5 then equate the exponents

6 - 2x = 2 ( subtract 6 from both sides )

- 2x = - 4 ( divide both sides by - 2 )

x = 2

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leonid [27]

Answer:

y=\sqrt{\frac{x^4-6x^2+12x+c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+c_1}{2}}

(Please vote me Brainliest if this helped!)

Step-by-step explanation:

\frac{dy}{dx}y=x^3+2x-5x+3

\mathrm{First\:order\:separable\:Ordinary\:Differential\:Equation}

  • \mathrm{A\:first\:order\:separable\:ODE\:has\:the\:form\:of}\:N\left(y\right)\cdot y'=M\left(x\right)

1. \mathrm{Substitute\quad }\frac{dy}{dx}\mathrm{\:with\:}y'\:

y'\:y=x^3+2x-5x+3

2. \mathrm{Rewrite\:in\:the\:form\:of\:a\:first\:order\:separable\:ODE}

yy'\:=x^3-3x+3

  • N\left(y\right)\cdot y'\:=M\left(x\right)
  • N\left(y\right)=y,\:\quad M\left(x\right)=x^3-3x+3

3. \mathrm{Solve\:}\:yy'\:=x^3-3x+3:\quad \frac{y^2}{2}=\frac{x^4}{4}-\frac{3x^2}{2}+3x+c_1

4. \mathrm{Isolate}\:y:\quad y=\sqrt{\frac{x^4-6x^2+12x+4c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+4c_1}{2}}

5. \mathrm{Simplify}

y=\sqrt{\frac{x^4-6x^2+12x+c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+c_1}{2}}

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Hope this helps.

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Step-by-step explanation:

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X + (x − 2) + (x − 4) = ? ;  In which
<span>
x + x </span>− 2 + x − 4 ; 

Combine the "like terms" ; 

  x + x + x = 3x ; 

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___________________________
The sum of three consecutive odd integers, in which "x" is the greatest integer;  is:  "3x − 6" .
_____________________________________________
Note:  The three consecutive odd integers, from least to greatest, are:

"(x − 4)" , "(x − 2)" , and "x" .

The sum is:  "(3x  − 6)<span>" .
</span>_____________________________________________
Note:  "(3x  − 6)" factors into:  " 3(x −2)" .

Note that:  " (x − 2) " is the second integer.
______________________________________________
So the sum total, which is:  "(3x  −  6)" ;  is 3 (three) times the value of the second integer; that is, "3 (x − 2)" .
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