Question

Determine the value of "x" from the following expression : 2^x*8^1/5=2^1/5
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Answer 1

Step-by-step explanation:

2^x × 8^1/5 = 2^1/5

2^x x 2^3/5 = 2^1/5

x + 3/5 = 2/5

x = -1/5

Answer 2

Answer:

x = -2/5

Step-by-step explanation:

Given :- The given expression is $2^{x} * 8^{\frac{1}{5} } = 2^{\frac{1}{5} }$

To Find :- The value of x in the above expression.

Solution :-

The given expression is $2^{x} * 8^{\frac{1}{5} } = 2^{\frac{1}{5} }$

Let's multiply 5 in the power on both sides,

$2^{5x}$ × $(8^{5} )^{\frac{1}{5} }$ = $(2^{5} )^{\frac{1}{5} }$

Now, the equation becomes

$2^{5x}$ × 8 = 2

⇒ $32^{x}$ × 8 = 2            [ ∵ $a^{bx}$ = $(a^{b^{x} })$ ]

⇒  $32^{x}$ = 2 ÷ 8

⇒  $32^{x}$ = 1/4

⇒ $2^{5x}$ = 1/$2^{2}$

⇒ $2^{5x}$ = $2^{-2}$

⇒ 5x = - 2       [∵ We know that we can equate the powers equal if the                    

                                                                                        base is same ]

⇒ x =  ( - 2/5 )

Therefore, x = -2/5 in the expression $2^{x} * 8^{\frac{1}{5} } = 2^{\frac{1}{5} }$.

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