If 576-2 a - 3 b -24 c- then a - b - c is-A- 6B- 8C- 9D- 10

The correct option is D 10Consider the equation 576=2^a× 3^b = 24^c. Prime factorisation nbsp;of 576 is given by 576 = 2 × 2 × 2 × 2 × 2 × 2× 3× 3 nbsp; ...

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Byju's Answer

Standard VIII

Mathematics

Exponent and Powers

If 576=2 a × ...

Question

If $576 = 2^{a} \times 3^{b} = 24^{c}$ , then $a + b + c$ is ___.

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Solution

The correct option is D 10
Consider the equation $576 = 2^{a} \times 3^{b} = 24^{c} .$
Prime factorisation of 576 is given by
$576 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$= 2^{6} \times 3^{2}$
Also, $576 = 24^{2} .$
$\Rightarrow a = 6$
$\Rightarrow b = 2$
$\Rightarrow c = 2$
Hence, $a + b + c = 10.$

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If 576=2a×3b=24c, then a+b+c is ___.

The correct option is D 10Consider the equation 576=2a×3b=24c. Prime factorisation of 576 is given by 576=2×2×2×2×2×2×3×3 =26×32 Also, 576=242. ⇒a=6 ⇒b=2 ⇒c=2 Hence, a+b+c=10.

If $576 = 2^{a} \times 3^{b} = 24^{c}$ , then $a + b + c$ is ___.