Can you help me find x? (Exponential Function).

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Can you help me find x? (Exponential Function).

$2^{x} - 10 (2^{- x}) + 3 = 0$ $2^x -10 (2^-x)+ 3 = 0$

2 Answers

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Answer 1 · 2017-04-13T11:56:45

$x = 1$ $x=1$

Explanation:

Multiplying each term of $2^{x} - 10 (2^{- x}) + 3 = 0$ $2^x-10(2^-x)+3=0$ by $2^{x}$ $2^x$ , we gwt

$2^{2 x} - 10 + 3 \times 2^{x} = 0$ $2^(2x)-10+3xx2^x=0$ .

Now let $2^{x} = u$ $2^x=u$ , the above becomes

$u^{2} + 3 u - 10 = 0$ $u^2+3u-10=0$

or $u^{2} + 5 u - 2 u - 10 = 0$ $u^2+5u-2u-10=0$

or $u (u + 5) - 2 (u + 5) = 0$ $u(u+5)-2(u+5)=0$

or $(u - 2) (u + 5) = 0$ $(u-2)(u+5)=0$

but as $u = 2^{x}$ $u=2^x$ , $u + 5 \neq 0$ $u+5!=0$ and dividing both sides by it, we get

$u = 2$ $u=2$ or $2^{x} = 2$ $2^x=2$ or $x = 1$ $x=1$

Answer 2 · 2017-04-13T12:20:35

$x = 1$ $x=1$

Explanation:

Write as: $2^{x} - \frac{10}{2^{x}} + 3 = 0$ $" "2^x-10/2^x+3" "=" "0$

$[2^{x} \times 1] - \frac{10}{2^{x}} + [3 \times 1] = 0$ $" "color(green)([2^xcolor(red)(xx1)] -10/2^x+[3color(red)(xx1)]" "=" "0$

$[2^{x} \times \frac{2^{x}}{2^{x}}] - \frac{10}{2^{x}} + [3 \times \frac{2^{x}}{2^{x}}] = 0$ $" "color(green)([2^xcolor(red)(xx2^x/2^x)] -10/2^x+[3color(red)(xx2^x/2^x)]=0$

$\frac{2^{2 x}}{2^{x}} - \frac{10}{2^{x}} + \frac{3 \times 2^{x}}{2^{x}} = 0$ $" "(2^(2x))/2^x" " -10/2^x+" "(3xx2^x)/2^x" "=" "0$

$2^{2 x} + (3 \times 2^{x}) - 10 = 0$ $" "2^(2x)+(3xx2^x)-10=0$

Changed my mind about the format. Write $2^{2 x} as {(2^{x})}^{2}$ $2^(2x) " as "(2^x)^2$

Set $a = 2^{x}$ $a=2^x$ giving

$a^{2} + 3 a - 10 = 0$ $a^2+3a-10=0$

$(a - 2) (a + 5) = 0$ $(a-2)(a+5)=0$

$a = - 2 and a = + 5$ $a=-2 and a=+5$

$\Rightarrow 2^{x} = + 2 and 2^{x} = - 5$ $=>2^x=+2 and 2^x=-5$

Using logs

Consider $2^{x} = 2$ $2^x=2$

$x ln (2) = ln (2) \Rightarrow x = \frac{ln (2)}{ln (2)} = 1$ $xln(2)=ln(2) => x=ln(2)/ln(2)=1$

Consider $2^{x} = - 5$ $2^x=-5$

$x ln (2) = ln (- 5)$ $xln(2)=ln(-5)$

but $ln (- 5)$ $ln(-5)$ is undefined so not a solution.

Thus $x = 1$ $x=1$

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Can you help me find x? (Exponential Function).

$2^{x} - 10 (2^{- x}) + 3 = 0$ $2^x -10 (2^-x)+ 3 = 0$

2 Answers

Explanation:

Explanation:

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Can you help me find x? (Exponential Function).

2x−10(2−x)+3=02^x -10 (2^-x)+ 3 = 0

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$2^{x} - 10 (2^{- x}) + 3 = 0$ $2^x -10 (2^-x)+ 3 = 0$