Math, asked by rahul1335, 1 year ago

4^x-4^x-1=24 then( 2x)^x=?

Answers

Answered by Anonymous

HEY mate here is your answer.

Hope it helps you..

^_^

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shadowsabers03: There is a mistake here. On a - (a/4) = 24, it becomes (4a - a)/4 = 24 and then 3a/4 = 24. We get 3a = 24 x 4 = 96. You didn't do 24 x 4 = 96.

shadowsabers03: So wrong answer, bro.

Anonymous: I think its crrt

shadowsabers03: No, it's wrong. Look at your answer carefully. a = 32, not 8.

Anonymous: yeah thanks

shadowsabers03: You're welcome.

shadowsabers03: x = 5/2.

Anonymous: yes

Anonymous: u r crrt

Answered by shadowsabers03

$4^x - 4^{x - 1} = 24 \\ \\ = 4^x - \frac{4^x}{4} = 24 \\ \\ = \frac{4^{x + 1} - 4^x}{4} = 24 \\ \\ 4^{x + 1} - 4^x = 24 * 4 = 96 \\ = 4^x * 4 - 4^x = 96 \\ = 4^x(4 - 1) = 96 \\ = 4^x * 3 = 96 \\ 4^x = \frac{96}{3} = 32 \\ \\ 4^x = 32 \\ = (2^2)^x = 2^5 \\ = 2^{2x} = 2^5 \\ \\ 2x = 5 \\ x = \frac{5}{2}$

$(2x)^x = (2 * \frac{5}{2})^{\frac{5}{2}} = 5^{\frac{5}{2}} \\ \\ = \sqrt{5^5} = \sqrt{5^4 * 5} = \sqrt{25^2 * 5} = 25\sqrt{5}$

The answer is 25√5.

Hope this may be helpful.

Please mark my answer as the brainliest if this helps you.

Thank you.

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