Home
Class 12
MATHS
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`

Text Solution

Verified by Experts

`1+xyz=1(log_(2a)a)(log_(3a)2a)(log_(4a)3a)`
`=1+(loga)/(log2a)(log2a)/(log3a)(log3a)/(log4a)`
`=1+(loga)/(log4a)`
`=log_(4a)4a+log_(4a)a`
`=log_(4a)4a^(2)=2log_(4a)2a`
`=2(log_(3a)2a)(log_(4a)3a)=2yz`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.38|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.39|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.36|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

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]

Home
Profile