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If 27^x=9/(3^x), find xdot...

If `27^x=9/(3^x),` find `xdot`

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To solve the equation \(27^x = \frac{9}{3^x}\), we will follow these steps: ### Step 1: Rewrite the bases as powers of 3 We know that: - \(27 = 3^3\) - \(9 = 3^2\) So, we can rewrite the equation: ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Show that : (x^(a(b-c)))/(x^(b(a-c)))*(x^b)/(x^a))^c=1 ((x^(a+b))...

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  2. If (9^nxx3^2xx(3^(-n/2))^(-2)-(27)^n)/(3^(3m)xx2^3)=1/(27), Prove th...

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  3. If 27^x=9/(3^x), find xdot

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  4. Find the values of x in each of the following : (i)2^(5x)-:2^x=(root(...

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  5. Evaluate each of the following: (i)5^2*5^4 (ii) 5^8+5^3 (iii) (3...

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  6. Evaluate each of the following: (i)(2/(11))^4*((11)/3)^2*(3/2)^3 (ii...

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  7. If a=2 and b=3, then find the values of each of the following: a^a+b^b...

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  8. Assuming that x , y are positive real numbers, simplify each of the fo...

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  9. Simplify : ((25)^(3/2)x(243)^(3/5))/((16)^(5/4)x(8)^(4/3))

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  10. Simplify: ((81)/(16))^(-3/4)xx[((25)/9)^(-3/2)-:(5/2)^(-3)]

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  11. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

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  12. Evaluate each of the following 5^2\xx\ 5^4 (ii) (3^2)^3 ​ ​ ​

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  13. Evaluate each of the following (i)((11)/(12))^3 (ii) (3/4)^(-3)

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  14. Evaluate each of the following: (i) (2/(11))^4 xx ((11)/3)^2 xx (3/2)...

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  15. Evaluate each of the following: (i)\ 2^(55)xx\ 2^(60)-\ 2^(97)xx\ 2^(...

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  16. If a=2 and b=3 , then find the values of each of the following: a^a+b^...

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  17. If a=2 and b=3 , then find the values of each of the following: (a/b)^...

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  18. Simplify the following (ii)(3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(18 ...

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  19. Simplify each of the following: (a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n...

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  20. If (9^n\ xx\ 3^2\ xx\ (3^(-n/2))^(-2)-\ 27^n)/(3^(3m)\ xx\ 2^3)=1/(27)...

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