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If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)...

If `x=(log)_(2a)a , y=(log)_(3a)2a ,z=(log)_(4a)3a ,p rov et h a t1+x y z=2y zdot`

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If x = log_(2a)a, y = log_(3a)2a , z = log_(4a)3a , then show that xyz + 1 = 2yz .

If x = log_(2a)^(a) , y = log_(3a)^(2a) and z = log_(4a)^(3a) show that xyz = 2yz - 1.

If x=log_(a)(bc),y=log_(b)(ca) and z=log_(c )(ab) show that x+y+z+2=xyz

If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y) , then prove that xyz = 1 .

If x = log_(c ) b + log_(b)c , y=log_(a)c + log_(c ) a, z=log_(b)a+log_(a)b , then show that x^(2) + y^(2) + z^(2) - 4 = xyz .

If x = log_(a)(bc), y = log_(b)(ca), z = log_(c)(ab) , then find 1/(x+1) + 1/(y+1) + 1/(z+1)

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b^2+bc+c^2).y^(c^2+ca+a^2).z^(a^2+ab+b^2)=1

If log_(3)x + log_(3)y =2 + log_(3)2 and log_(3)(x+y) =2 , then

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1

If x = log_(a)^(bc) , y = log_(b)^(ca) and z = log_(c)^(ab) then show that frac(1)(x+1)+frac(1)(y+1)+frac(1)(z+1) = 1 , [abc ne 1]

CENGAGE PUBLICATION-LOGARITHM-All Questions
  1. If P is the number of natural numbers whose logarithms to the base 10 ...

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  2. Find the compound interest on Rs. 12000 for 10 years at the rate of 12...

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  3. If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,p rov et h a t1+x y z=...

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  4. Let L denote antilog32 0.6 and M denote the number of positive integer...

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  5. Let x=(0. 15)^(20)dot Find the characteristic and mantissa of the loga...

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  6. Using logarithms, find the value of 6.45 x 981.4

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  7. In the 2001 census, the population of India was found to be 8. 7x10^7d...

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  8. If (log)(10)2=0. 30103 ,(log)(10)3=0. 47712 , then find the number of...

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

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  10. Solve the equations for x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) ...

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  11. The real solutions of the equation 2^(x+2). 5^(6-x)=10^(x^2) is/are 1 ...

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  12. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to

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  13. If p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x), then

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  14. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is

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  15. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

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  16. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

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  17. Solve the following equation of x :2(log)x a+(log)(a x)a+3(log)(a^2x)a...

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

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  19. Which of the following, when simplified, reduces to unity?

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  20. If (log)a x=b for permissible values of a and x , then identify the ...

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