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The `x , y , z` are positive real numbers such that `(log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3,` then the value of `(1/(2z))` is ............

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The correct Answer is:
5
` z = 8x^(3), z = 5^(6)y^(6), z = x^(2//3) y^(2//3)`
` rArr x = (z^(1//3))/2, y = (z^(1//6))/5`
` rArr z = 1/(2^(2//3)) z^(2//9) * (z^(2//18))/(5^(2//3))`
` rArr z^(2//3) = 1/((10)^(2//3)) or z = 1/(10)`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Numerical)
  1. If log(a)b=2, log(b)c=2, and log(3) c= 3 + log(3) a,then the value of...

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  2. The value of (log(10)2)^(3)+log(10)8 * log(10) 5 + (log(10)5)^(3) is .

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  3. If log(4)A=log(6)B=log(9)(A+B)," then "[4(B//A)]("where "[*] represent...

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  4. Integral value of x which satisfies the equation =log6 54+(log)x 16=(l...

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  5. If a = log(245) 175 and b = log(1715) 875, then the value of (1-ab)/...

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  6. The difference of roots of the equation (log(27)x^(3))^(2) = log(270x^...

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  7. Sum of integral values of x satisfying the inequality 3^((5/2)log3(12-...

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  8. The least integer greater than log(2) 15* log(1//6 2* log(3) 1//6 is ...

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  9. The reciprocal of 2/(log(4)(2000)^(6))+3/(log(5)(2000)^(6)) is .

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  10. Sum of integers satisfying sqrt(log(2)x-1)-1//2 log(2)(x^(3))+2 gt 0 ...

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  11. Number of integers satisfying the inequality log(1//2)|x-3| gt -1 i...

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  12. Number of integers le 10 satisfying the inequality 2 log(1//2) (x-1)...

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  13. The value of (sqrt(3+2sqrt2)+sqrt(3-2sqrt2))^(2^(9)) is .

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  14. The value of 5^((log)(1/5)(1/2))+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(lo...

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  15. The value of N=((log)5 250)/((log)(50)5)-((log)5 10)/((log)(1250)5) is...

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  16. if x+log10 (1+2^x)=xlog10 5+log10 6 then x

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  17. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

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  18. If a=log(12)18 and b=log(24)54 then find the value of ab+5(a-b)

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