Question

Root 2 to power x is equal to 64 find x

Answer 1

Answer:

x = 12

Step-by-step explanation:

Write the square root as exponent:

(2) x/2 = 64

Write 64 as 2^6:

(2) x/2 = 2^6

Since both numbers are 2, the exponents are equal:

x/2 = 6

Multiply 2 on both sides:

x = 12.

Answer 2

12 is the value of x:

Given:

$\sqrt{2} ^{x}$ = 64

To find:

the value of x.

Solution:

Since we have the equation of root 2 to power x is equal to 64, we write it in the following numerical form:

$\sqrt{2} ^{x}$ = 64

Now, since 64 can be written in the terms of 2, we will then write 2 raised to the respective number that results in 64.

$\sqrt{2}^{x}$ = $2^{6}$

Thus, we have gotten similar numerals on both sides but one still has a root, so now we remove the root. and (write in terms of $2^1$ = 2$2^{\frac{1}{2} }$)

$2^{\frac{x}{2} }$ = $2^6$

If,

a$a^{x} = a^{y} \\then,\\x = y$

Therefore,

$\frac{x}{2} = 6$

x = 6 × 2

X = 12

Therefore the value of x will be 12.

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