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`

A

2yz

B

2xy

C

2zx

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A

We have,
`xyz + 1 = "log"_(2a) a xx "log"_(3a) 2a xx "log"_(3a) 4a + 1`
`rArr xyz + 1 = "log" _(4a) a+ 1`
`rArr xyz + 1 = "log"_(4a) a + "log"_(4a) 4a = "log"_(4a) (2a)^(2)`
`rArr xyz + 1 = "log"_(4a) (2a)^(2) = 2"log"_(4a) 2a = 2 "log"_(3a) 2a xx "log"_(4a) 3a`
`rArr xyz + 1 = 2yz`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

LOGARITHMS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos
LOGARITHMS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|66 Videos
LOGARITHMS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos
INEQUALITIES
OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos
MATRICES
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

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

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If (log x)/(y-z)=(logy)/(z-x) =(logz)/(x-y) , then prove that: x^x y^y z^z=1

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

if x =log_a (bc), y= log_b (ca) and z=log_c(ab) then 1/(x+1)+1/(y+1)+1/(z+1)

If log_(2)(x + y) = log_(3)(x - y) = (log 25)/(log 0.2) , find the values of x and y.

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 ............

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 ............

If (log)_3y=xa n d(log)_2z=x , find 72^x in terms of yand zdot

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))

OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs

If a, b, c are positive real numbers, then a^("log"b-"log"c) xx b^(...
Text Solution
|
The value of (bc)^log(b/c)*(ca)^log(c/a)*(ab)^log(a/b) is
Text Solution
|
If x=(log)(2a)a , y=(log)(3a)2a ,z=(log)(4a)3a ,p rov et h a t1+x y z=...
Text Solution
|
Evaluate : (1)/(log(a)bc + 1) + (1)/(log(b)ca + 1) + (1)/(log(c) ab ...
Text Solution
|
If y=a^(1/(1-(log)a x))a n dz=a^(1/(1-(log)a y)),t h e np rov et h a t...
Text Solution
|
If a = "log"2, b = "log" 3, c ="log" 7 " and " 6^(x) = 7^(x+4) then x=
Text Solution
|
Given a^2+b^2=c^2&\ a .0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ prove that ...
Text Solution
|
If 5^x=(0. 5)^y=1000 , then 1/x-1/y=
Text Solution
|
Solve for x :4^x3^(x-1//2)=3^(x+1//2)-2^(2x-1) .
Text Solution
|
If (logx)/(2a+3b-5c)=(log y)/(2b+3c-5a)=(log z)/(2c=3a-5b') then xyz=
Text Solution
|
I flogx=(logy)/2=(logz)/5, th ten x^4y^3z^(- 2)=
Text Solution
|
If loga=1/2 logb=1/5logc then a^4b^3c^(-2)=
Text Solution
|
If a=log(24)12,b=log(48)36 and c=log(36)24, abc is equal to
Text Solution
|
If a,b,c are any three consecutive integers , prove that log(1+ac)=2lo...
Text Solution
|
If ("log"(a)x)/("log"(ab)x) = 4 + k + "log"(a)b, "then" k=
Text Solution
|
If a = 1 + log(x) yz, b = 1 + log(y) zx and c = 1 + log xy where x, ...
Text Solution
|
(1)/("log"(2)n) + (1)/("log"(3)n) + (1)/("log"(4)n) + … + (1)/("log"(4...
Text Solution
|
If n is a natural number such that n=P1^(a1)P2^(a2)P3^(a3)...Pk^(ak) ...
Text Solution
|
Prove that number (log)2 7 is an irrational number.
Text Solution
|
If in a right angled triangle, a\ a n d\ b are the lengths of sides...
Text Solution
|