Find the value of x if 26- 22 x-210

The correct option is B x=2Using Laws of Exponents, we know that nbsp;a^m× a^n=a^m+n ⇒ nbsp;2^6 × 2^2x=2^6+2x ⇒ 2^6+2x=2^10 ⇒ 6+2x=10 Since the bases ...

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Standard VII

Mathematics

Multiplying Terms with the Same Base

Find the valu...

Question

Find the value of x if $2^{6} \times 2^{2 x} = 2^{10}$

x=1

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x=2

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x=3

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x=4

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Solution

The correct option is B x=2
Using Laws of Exponents, we know that $a^{m} \times a^{n} = a^{m + n}$
$\Rightarrow$ $2^{6} \times 2^{2 x} = 2^{6 + 2 x}$
$\Rightarrow$ $2^{6 + 2 x} = 2^{10}$
$\Rightarrow$ 6+2x=10
Since the bases are same equating the powers we get,
$2 x = 4 \Rightarrow x = 2$

Suggest Corrections

Find the value of x if 26×22x=210

The correct option is B x=2Using Laws of Exponents, we know that am×an=am+n ⇒ 26×22x=26+2x ⇒ 26+2x=210 ​​​​​​⇒ 6+2x=10 Since the bases are same equating the powers we get, 2x=4⇒x=2

Find the value of x if $2^{6} \times 2^{2 x} = 2^{10}$

The correct option is B x=2
Using Laws of Exponents, we know that $a^{m} \times a^{n} = a^{m + n}$
$\Rightarrow$ $2^{6} \times 2^{2 x} = 2^{6 + 2 x}$
$\Rightarrow$ $2^{6 + 2 x} = 2^{10}$
$\Rightarrow$ 6+2x=10
Since the bases are same equating the powers we get,
$2 x = 4 \Rightarrow x = 2$