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

If `2^x = 3^y =12^z` show that `1/z= 1/y+2/x`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Show that: ((a^(x+1))/(a^(y+1)))^(x+y)\ ((a^(y+2))/(a^(z+2)))^(y+z)\ (...

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

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

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

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

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

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

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  8. Find the values of x in each of the following : (i)2^(5x)-:2^x=2^(20/...

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

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  10. Find the value of x in each of the following: 2^(x-7)\ xx\ 5^(x-4)=125...

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

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

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

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

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

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

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

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  18. If a and b are distinct positive primes such that root(3)(a^6b^(-4))...

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  19. If a\ a n d\ b are different positive primes such that (i)\ ((a^(-1)\ ...

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  20. If 2^x\ 3^y\ 5^z=2160\ , find x ,\ y\ a n d\ z . Hence, compute the va...

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