Question

2^5×2^k=256

find k

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Answer 1

2^5 *2^k=256

2^(5+k)=2^8

5+k= 8

k=8-5=3

Answer 2

Answer:

$\large{\underline{\boxed{\sf k = 3 }}}$

Step-by-step explanation:

$\sf 2 {}^{5} \times 2 {}^{k} = 256 \\ \\ \implies \sf 2 {}^{5} \times 2 {}^{k} = 2 {}^{8}$

Now, we know that ;

$\boxed{ \sf a {}^{m} \times a {}^{n} = a {}^{m + n}}$

$\implies \sf 2 {}^{5} \times 2 {}^{k} = 2 {}^{8} \\ \\ \implies \sf 2 {}^{5 + k} = 2 {}^{8}$

As both sides, bases are same, so cancelling 2 both sides, we get -

$\implies \sf 5 + k = 8 \\ \\ \implies \sf k = 8 - 5 \\ \\ \boxed{ \bf \therefore k = 3}$

Thus, the answer is 3.

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Verification:

$\sf 2 {}^{5} \times 2 {}^{k} = 256 \\ \\ \implies \sf 2 {}^{5} \times 2 {}^{3} = 256 \\ \\ \implies \sf 32 \times 8 = 256 \\ \\ \implies \sf 256 = 256 \\ \\ \bf \therefore LHS = RHS$

Hence, the answer is 3.