If -1024-3- 8-x- then x is - 5-10-2-15-

The correct option is A 5 Given: (√(1024))^3= 8^x ⇒ (√(()2^10))^3 = 8^x. nbsp; nbsp; ⇒ (√(()(2^5)^2))^3=8^x. nbsp; as nbsp;(a^m)^n=a^mn ⇒ (2^5)^3=(2^ ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents

If (√(1024))^...

Question

$If {(\sqrt{1024})}^{3} = 8^{x}, then x is$ ________.

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Solution

The correct option is A
5

Given:
${(\sqrt{1024})}^{3} = 8^{x}$

$\Rightarrow (\sqrt{(} 2^{10}))^{3} = 8^{x}$ .

$\Rightarrow (\sqrt{(} (2^{5})^{2}))^{3} = 8^{x}$ . {as ${(a^{m})}^{n}$ = $a^{m n}$ }

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

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

$\Rightarrow (8)^{5}$ = $(8)^{x}$

We know that, if $a^{n}$ = $a^{m}$ then, $n = m$ .

Hence,
$\Rightarrow x = 5$

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If (√1024)3=8x, then x is ________.

The correct option is A 5 Given: (√1024)3=8x ⇒(√(210))3=8x. ⇒(√((25)2))3=8x. {as (am)n=amn} ⇒(25)3=(23)x ⇒(23)5=(23)x ⇒(8)5= (8)x We know that, if an= am then, n=m. Hence, ⇒x=5

$If {(\sqrt{1024})}^{3} = 8^{x}, then x is$ ________.