Question

Find the value of the unknown constant . The sum is in the picture​

Answer 1

Answer:

$x = 5$

Step-by-step explanation:

$2 {}^{4 - 3x} \div 2 {}^{2 - x} = 2 {}^{ - 8}$

$\frac{2 {}^{4 - 3x} }{2 {}^{2 - x} } = \frac{1}{2 {}^{8} }$

$2 {}^{4 - 3x - 2 + x} = \frac{1}{2 {}^{8} }$

$2 {}^{2 - 2x} = \frac{1}{256}$

$2 {}^{2 - 2x} = 2 {}^{ - 8}$

$2 - 2x = - 8$

$- 2x = - 8 - 2$

$- 2x = - 10$

$x = \frac{ 10}{2}$

$x = 5$

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Answer 2

Step-by-step explanation:

${ \huge{ \pink{ \underline{ \underline{ \mathbb{QUESTION: }}}}}}$

Find the value of the unknown constant .

$\displaystyle{ \sf{ {2}^{4 - 3x} \div {2}^{2 - x} = {2}^{ - 8} }}$

${ \huge{ \pink{ \underline{ \underline{ \mathbb{ SOLUTION : }}}}}}$

◘ As the bases are same so we can directly equate with the powers.

As we know that,

$\sf { {a}^{m} \div {a}^{n} = {a}^{m - n} }$

$\displaystyle{ \sf{ : \implies \: (4 - 3x) - (2 - x) = - 8}}$

$\displaystyle{ \sf{ : \implies \: 4 - 3x - 2 + x = - 8}}$

$\displaystyle{ \sf{ : \implies \: 4 - 2 - 3x + x = - 8}}$

$\displaystyle{ \sf{ : \implies2 - 2x = - 8}}$

$\displaystyle{ \sf{ : \implies \: -2x = - 8 - 2}}$

$\displaystyle{ \sf{ : \implies \: -2x = - 10}}$

$\displaystyle{ \sf{ : \implies \: x = \cancel\frac{ - 10}{-2} }}$

$\displaystyle{ \sf{ : \implies \: x = 5 }}$

• Value of the unknown constant is 5.

${ \huge{ \pink{ \underline{ \underline{ \mathbb{ MORE \: TO \: KNOW : }}}}}}$

✪ A number on its own is called a Constant.

✪ An expression is a mathematical statement without an equal-to sign (=).

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$