Question

Find the value of n in 5^2n X 5^3 = 5^11

Answer 1

ANSWER.

• The value of n is 4.

SOLUTION.

Given –

$\tt \implies {5}^{2n} \times {5}^{3} = {5}^{11}$

We know that,

$\tt \implies {x}^{a} \times {x}^{b} = {x}^{a + b}$

Therefore,

$\tt \implies {5}^{2n + 3} = {5}^{11}$

Also,

$\tt \implies {x}^{a} = {x}^{b}$

$\tt \implies a = b$

Therefore,

$\tt \implies 2n + 3 = 11$

$\tt \implies 2n =8$

$\tt \implies n =4$

★ So, the value of n is 4.

VERIFICATION.

Taking LHS, we get,

$\tt = {5}^{2n} \times {5}^{3}$

$\tt = {5}^{2 \times 4} \times {5}^{3}$

$\tt = {5}^{8} \times {5}^{3}$

$\tt = {5}^{11}$

= RHS.

Hence, our answer is correct (Verified)

Answer 2

Answer:

4 is your answer of the question