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# help with algebra

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Solve the equation: ${ 2 }^{ x }+{ 2 }^{ x+1 }+{ 2 }^{ x+2 }+{ 2 }^{ x+3 }=\frac { 15 }{ 2 }$.

Jan 23, 2021

#1
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15/2 = 7.5

Adding multiples of 2 we can never get 1/2 unless we use an exponent of -1 at one point.

Having exponents smaller would result in longer decimals(.25,.125) So x has to be -1

Checking we get

2^-1+2^0+2^1+2^2

1/2+1+2+4

1/2+7

7.5

Jan 23, 2021
#2
+31703
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Here's another way of looking at it:

Jan 23, 2021
#3
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just ignore the base and just look at the exponent

so the equation becomes (x)+(x+1)+(x+2)+(x+3)=15/2.

combine like terms -> 4x+6=15/2

subtract 6 from both sides and divide both sides by 4 to get x=3/8

Jan 24, 2021
#4
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$$2^x+2^{x+1}+2^{x+2}+2^{x+3}=\frac{15}{2}$$

$$15\cdot \:2^x=\frac{15}{2}$$
$$\frac{15\cdot \:2^x}{15}=\frac{\frac{15}{2}}{15}$$

$$2^x=\frac{1}{2}$$

$$x=-1$$

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Jan 24, 2021