First, we'll re-write the equation, using the negative
power property of exponential functions.
`2^x -
14/(2^x)=-5`
We'll multiply by `2^x ` both
sides:
`2^2x - 14 =
-5*2^x`
We'll move all terms to one
side:
`2^2x + 5*2^x - 14 =
0`
We'll treat the equation above as a quadratic equation
and we'll solve it using quadratic formula, `2^x ` being the
unknown:
`2^x = (-5+sqrt(25 +
56))/2`
`` `2^x =
(-5+sqrt81)/2`
`2^x =
(-5+9)/2`
`2^x = 2` => x =
1
`2^x = (-5-9)/2`
`2^x` = -7
impossible since 2^x > 0 for any real value of
x.
Therefore, the equation will have only one
solution: x = 1.
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