Question

(2 ^(x+3)) whole root =16 find x

Answer 1

(2^(x+3))²=16

2^2x+6=2^4

2x+6=4

2x=4-6

x= -2/2

x= -1

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Answer 2

The value of x is 5.

Step-by-step explanation:

We are given,

$\sqrt{2^{x+3} }=16$

and we have to find the value of x.

• Calculation for x

we have

$\sqrt{2^{x+3} }=16$  or  $({2^{x+3} )^{\frac{1}{2} } }=16$

for solving this question first do squaring on both sides,

$(({2^{x+3} )^{\frac{1}{2} } })^{2} =(16)^{2}$

we get,

${2^{x+3} }=(16)^{2}$

and we can write 16 as $2*2*2*2 =16$

or $16=2^{4}$

${2^{x+3} }=(2^{4} )^{2}$

${2^{x+3} }=2^{8}$

now the base of both powers are same on the both sides so we can equate them as,

$x+3=8$

$x=8-3$

$x=5$.

We get the value of x as 5.