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If 4^x-\ 4^(x-1)=24 , then (2x)^x equals...

If `4^x-\ 4^(x-1)=24 ,` then `(2x)^x` equals `5sqrt(5)` (b) `sqrt(5)` (c) `25sqrt(5)` (d) `125`

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To solve the equation \(4^x - 4^{x-1} = 24\), we can follow these steps: ### Step 1: Rewrite the equation We start with the equation: \[ 4^x - 4^{x-1} = 24 \] Using the property of exponents, we can rewrite \(4^{x-1}\) as \(\frac{4^x}{4}\): ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. If g=t^(2/3)+\ 4t^(-1/2) , what is the value of g when t=64 ?

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  2. If x^(-2)=64 , then x^(1/3)+\ x^0= (a) 2 (b) 3 (c) 3/2 (d) 2/3

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  3. If 4^x-\ 4^(x-1)=24 , then (2x)^x equals 5sqrt(5) (b) sqrt(5) (c...

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  4. When simplified (-1/(27))^(-2/3) is 9 (b) -9 (c) 1/9 (d) -1/9

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  5. Which one of the following is not equal to root(3)(8)^(-1/2)\ ? (a)r...

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  6. Which one of the following is not equal to ((100)/9)^(-3/2) ? (a)\ (9/...

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  7. When simplified (256)^-(4^((-3//2)\ )) is 8 (b) 1/8 (c) 2 (d) 1...

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  8. (5^(n+2) −6 xx 5^(n+1))/(3 xx 5^n − 2xx 5^(n+1)) is equal to ...

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  9. If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt...

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  10. If (3^(2x-8))/(225)=(5^3)/(5^x) , then x= 2 (b) 3 (c) 5 (d) 4

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  11. If (2/3)^x\ \ (3/2)^(2x)=(81)/(16), . then x= 2 (b) 3 (c) 4 (d)...

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  12. If a ,\ b ,\ c are positive real numbers, then root(5)(3125\ a^(10)b^5...

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  13. The value of 64^(-1/3)\ (64^(1/3)-64^(2/3)), is 1 (b) 1/3 (c) -...

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  14. If sqrt(5^n)=125 , then 5^(nsqrt64 )= 25 (b) 1/(125) (c) 625 (d)...

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  15. If (16)^(2x+3)=(64)^(x+3), then 4^(2x-2)=64(b) 256 (c) 32 (d) 512

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  16. If a ,\ m ,\ n are positive integers, then {root(m)(sqrt a)}^(m n) is ...

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  17. If 2^(-m)\ xx1/(2^m)=1/4, then 1/(14)\ {(4^m)^(1//2)+\ (1/(5^m))^(-1)}...

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  18. If x=2\ \ and y=4, then (x/y)^(x-y)+\ (y/x)^(y-x)=

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  19. The value of m for which [{(1/(7^2))^(-2)}^(-1/3)]^(1/4)=7^m ,

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  20. If (2^(m+n))/(2^(m-n))=16 and a=2^(1/10) then ((a^(2m+n-p))^2)/((a^(m-...

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