Question

^ =power
Find value of k if
A)2^5×2^k=256
B)3^k×9=3^13

Answer 1

Answer:

A)k=3

B)k=11

Step-by-step explanation:

A)2^5*2^k=256

2^5*2^k=2^8

5+k=8

k=3

B)3^k*3^2=3^13

k+2=13

k=11

Answer 2

A. The value of k is equal to 3.

B. Thus, the value of k is equal to 11.

Step-by-step explanation:

A) We have,

$2^5\times 2^k=256$

To find, the value of k = ?

∴ $2^5\times 2^k=256$

Using the identity,

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

⇒ $2^{5+k}=2^8$

Equating the powers, we get

5 + k = 8

⇒ k = 8 - 5 = 3

Thus, the value of k is equal to 3.

B) We have,

$3^k\times 9=3^{13}$

To find, the value of k = ?

∴ $3^k\times 9=3^{13}$

⇒ $3^k\times 3^2=3^{13}$

Using the identity,

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

⇒ $3^{k+2}=3^{13}$

Equating the powers, we get

k + 2 = 13

⇒ k = 13 - 2 = 11

Thus, the value of k is equal to 11.