Question

If √2ⁿ = 1024, find the value of 3² × n
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MrCoronaVirus

Answer 1

Given

• √2ⁿ = 1024

To find

• 3² × n

Solution

• √2ⁿ = 1024
• (2ⁿ)½ = (2)¹⁰
• 2ⁿ/² = 2¹⁰
• n/2 = 10
• n = 10×2
• n = 20

∅ Value of n is 20

• 3² × n
• 3² × 20
• 9  × 20
• 180

⇰ The value of 3² × n where n is 20 is 180

Answer 2

√2^n = 1024

√2^n = 32 × 32

√2^n = 2^5 × 2^5

√2^n = √2^10 × √2^10

√2^n = √2^20

Since base is same, we can write the above as,

n = 20

••••••••••••••••••••

= 3² × n

= 3² × 20

= 9 × 20

= 180