Question

If 2^x+3 + 2^x – 4 =129, then find the value of x.

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

$\sf{ Solve \: for \: x \: when \: \: \: {2}^{(x + 3)} + {2}^{(x - 4)} = 129 \: }$

CALCULATION

$\sf{ {2}^{(x + 3)} + {2}^{(x - 4)} = 129 }$

$\displaystyle \implies \: \sf{( {2}^{x} \times {2}^{3} ) + \frac{{2}^{x}}{ {2}^{4} } = 129 } \: \: ....(1)$

$\sf{ Let \: \: y = {2}^{x} \: } \: \:$

Then Equation ( 1 ) becomes

$\displaystyle \: \sf{8y + \frac{y}{16} = 129 }$

$\implies \: \displaystyle \: \sf{ \frac{128y + y}{16} = 129 }$

$\implies \: \displaystyle \: \sf{ \frac{129y }{16} = 129 }$

$\implies \: \displaystyle \: \sf{ y =129 \times \frac{16}{129} }$

$\implies \: \displaystyle \: \sf{ y =16 }$

$\implies \: \displaystyle \: \sf{ {2}^{x} =16 }$

$\implies \: \displaystyle \: \sf{ {2}^{x} = {2}^{4} }$

$\implies \: \displaystyle \: \sf{ x = 4 }$

RESULT

$\boxed{ \sf{ \: \:x = 4 \: \: }}$

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Answer 2

We have:

$2^{x+3} +2^{x-4} =129$

We have to find, the value of x in the given expression.

Solution:

∴ $2^{x+3} +2^{x-4} =129$

⇒ $2^{x}2^{3} +\dfrac{2^{x}}{2^{4}} =129$

⇒ $2^{x}(8 +\dfrac{1}{16} )=129$

⇒ $2^{x}(\dfrac{128+1}{16} )=129$

⇒ $2^{x}(\dfrac{129}{16} )=129$

⇒ $2^{x}=16$

⇒ $2^{x}=2^4$

Comparing both sides the powers, we get

x = 4

Thus, the value of x is the given expression is "equal to 4".