If 96 - x6- 546- then the value of x is -

Given, 9^6 × x^6= 54^6. Since for a nbsp;non zero integer a and integers m and n, a^m× b^m = ab^m, ∴ 9^6× x^6 = (9× x)^6 = (9x)^6 (9x)^6= 54^6 As powers ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If 96 × x6= 5...

Question

If $9^{6} \times x^{6} = 54^{6},$ then the value of $x$ is ___.

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Solution

The correct option is A 6
Given, $9^{6} \times x^{6} = 54^{6} .$

Since for a non-zero integer $a$ and integers $m$ and $n$ ,

$a^{m} \times b^{m} = a b^{m},$

$∴ 9^{6} \times x^{6} = (9 \times x)^{6} = (9 x)^{6}$

$⟹ {(9 x)}^{6} = 54^{6}$

As powers are equal on the both sides, we equate the bases to get:

$9 x = 54$

$\Rightarrow x = \frac{54}{9} = 6$

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If 96×x6=546, then the value of x is ___.

The correct option is A 6Given, 96×x6=546. Since for a non-zero integer a and integers m and n, am×bm=abm, ∴96×x6=(9×x)6=(9x)6 ⟹(9x)6=546 As powers are equal on the both sides, we equate the bases to get: 9x=54 ⇒x=549=6

If $9^{6} \times x^{6} = 54^{6},$ then the value of $x$ is ___.