Question

find the value of x in this question.

Answer 1

8^255 = ( 32 )^x
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(2 × 2 × 2 )^255 = (2 × 2 × 2 × 2 × 2 )^x

(2^3 )^255 = ( 2^5 )^x

2^( 3 × 255 ) = 2^( 5 × x )

2^(765) = 2^(5x)

since ,both sides base are equal , then it will get cancel with each other. now we have ,

765 = 5x

x = 153

therefore , value of x = 153

Answer : x = 153

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Answer 2

Hey there!

Given equation to simplify and subsequently find the final value for the variable "x":

$\bf{8^{255} = (32)^x}$

Now, convert the following base of "8^255" to the base of "2" and the inner exponential power "3" that is:

$\bf{(2^3)^{255} = 32^x}$

Now, convert the base of "32^x" to the power of "5" and base of "2":

$\bf{(2^3)^{255} = (2^5)^x}$

Apply the rule of exponents into this newly formed gisted value that is;

$\boxed{\bf{(a^b)^c = a^{b \times c}}}$

Here, $\bf{(2^5)^x = 2^{5x}, \quad (2^3)^{255} = 2^{3 \times 255}}$

$\bf{\therefore \quad 2^{3 \times 255} = 2^{5x}}$

Now, cancel out or balance the similar bases by functions of a specific variable that is,

$\bf{a^{f(x)} = a^{g(x)}, \quad then, \: \: f(x) = g(x)}$

$\bf{\therefore \quad 3 \times 255 = 5x}$

$\bf{\therefore \quad 765 = 5x}$

Switch the following sides and divide both the sides with the value of "5" to get the product on R.H.S.:

$\bf{\therefore \quad \dfrac{5x}{5} = \dfrac{765}{5}}$

$\boxed{\bf{\underline{\therefore \quad x = 153}}}$

Which is the required answer for this type of query.

Hope this helps you and solves the doubts for finding exponential variable values with a given condition on each side!!!!!