Question

$find \: the \: value \: of \: x \: if \: 2^x + 2 ^x + 2^x = 192$

Answer 1

Given that

2ˣ + 2ˣ + 2ˣ = 192

⇒ 3(2ˣ) = 192

⇒ 2ˣ = 192/3

⇒ 2ˣ = 64

⇒ 2ˣ = 2⁶

⇒ x = 6                    [ If xᵃ = xᵇ  ⇒ a = b ]

Answer 2

x = 6

Step-by-step explanation:

We need to find the value of x if $2^x+2^2+2^x=192$

Taking $2^x$ common from the above equation.

$2^x(1+1+1)=192\\\\2^x(3)=192\\\\2^x=\dfrac{192}{3}\\\\2^x=64$

We know that, $2^6=64$

$2^x=2^6$

If $a^b=p^b\ \text{then}\ b=p$

x = 6

So, the value of x is 6.

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