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Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(...

Show that: `((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+a)=1`

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LHS`=(3^(a-b))^(a+b)(3^(b-c))^(b+c)(3^(c-a))^(c+a)`
`=3^(a^2-b^2+b^2-c^2+c^2-a^2)`
`=3^0`
`=1=RHS`
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

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  2. Show that:(a^(x-y))^(x+y).(a^(y-z))^(y+z).(x^(z-x))^(z+x)=1

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  3. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

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  4. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x ​ ​

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  5. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

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  6. If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

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  7. If 3^x=5^y=(75)^z show that z=(xy)/(2x+y

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

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  9. Find the values of x in each of the following : (i)2^(5x)-:2^x=25^(2...

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  10. Find the value of x in each of the following: (i)\ (3/5)^x\ (5/3)^(2x)...

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  11. Find the value of x in each of the following: (i)2^(x-7) xx 5^(x-4)=1...

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  12. Find the value of x in each of the following: (i)\ 5^(2x+3)=1 (ii)\ ...

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  13. If x=2^(1/3)+ 2^(2/3) show that x^3-6x=6

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  14. Determine (8x)^x , if 9^(x+2)=240+9^x

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  15. If 3^(x+1)=9^(x-2), find the value of 2^(1+x)

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  16. If 3^(4x)=(81)^(-1) and 10^(1/y)=0. 0001 , find the value of 2^(-x+4y)

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  17. If 5^(3x)=\ 125\ and 10^y=0. 001 find x\ a n d\ y C

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  18. .Solve the following equations: (i)\ 3^(x+1)=27\ xx\ 3^4 \ (ii)4^(...

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  19. If a\ a n d\ b are distinct positive primes such that root(3)(a^6b^(-4...

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  20. If a and b are different positive primes such that (i)\ ((a^(-1)\ b^2)...

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