Home
Class 12
MATHS
If y^2=x za n da^x=b^y=c^z , then prove ...

If `y^2=x za n da^x=b^y=c^z ,` then prove that `(log)_6a=(log)_c bdot`

Text Solution

Verified by Experts

`a^(x) = b^(y) = c^(z)`
` rArr x log a = y log b = z log c`
` :. y/x = z/y rArr(log a)/(log b) = (log b)/(log c)`
` rArr log_(b) a = log_(c) b`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.4|12 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.5|13 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.2|9 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If x ,y ,z are in G.P. and a^x=b^y=c^z , then (log)_b a=(log)_a c b. (log)_c b=(log)_a c c. (log)_b a=(log)_c b d. none of these

f x^(2) + y^(2)= 25xy , then prove that 2 log(x + y) = 3log3 + logx + logy.

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If a, b, c are in geometric progression, and if a^(1/x)=b^(1/y)=c^(1/z) , then prove that x, y, z are in arithmetic progression.

If y=a^(1/(1-(log)_a x)) and z=a^(1/(1-(log)_a y)) ,then prove that x=a^(1/(1-(log)_a z))

If a,b,c are in geometric progression, and if a^(1/x) = b^(1/y) =c^(1/z) , then prove that x,y,z arithmetic progression.

If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

If a,b,c are in geometric progression and if a^((1)/(x))=b^((1)/(y))=c^((1)/(z)) , then prove that x,y,z are in arithmetic progression.

If a,b,c are in G.P and a^(1/x) = b^(1/y) = c^(1/z) , prove that x,y,z are in A.P.