Exponents

Algebra Level 3

If 4 x = 1024 4^x= 1024 then ( 4 x + 1 ) ( 5 x − 1 ) = ? (4^{x+1})(5^{x-1})=?

A. 1 0 6 10^6

B. 5 4 × 1 0 5 5^4\times 10^5

C. 4 4 × 1 0 5 4^4\times 10^5

D. 5 4 × 1 0 4 5^4\times 10^4

E. 4 4 × 1 0 4 4^4\times 10^4

B A E D C

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Maximos Stratis
Jun 9, 2017

It is true that:
2 10 = 1024 ⇒ 4 5 = 4 x ⇒ x = 5 2^{10}=1024\Rightarrow 4^{5}=4^{x}\Rightarrow x=5
So:
4 x + 1 5 x − 1 = 4 6 5 4 = 4 6 ( 10 2 ) 4 = 4 6 1 0 4 2 4 = 4 6 1 0 4 4 2 = 4 4 1 0 4 4^{x+1}5^{x-1}=4^{6}5^{4}=4^{6}(\frac{10}{2})^{4}=4^{6}\frac{10^{4}}{2^{4}}=4^{6}\frac{10^{4}}{4^{2}}=4^{4}10^{4}
Therefore, option E \boxed{E} is correct.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for posting a solution. No doubt it is correct.

Hana Wehbi - 4 years ago

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