Home
Class 12
MATHS
(2^(log6 18))*(3^(log6 3))...

`(2^(log_6 18))*(3^(log_6 3))`

A

6

B

9

C

12

D

18

Text Solution

Verified by Experts

The correct Answer is:
A
`(2^(log_(6)18)).(3^(log_(6)3))`
`=(2^(log_(6)6+log_(6)3)).(3^(log_(6)3))`
`=2(2^(log_(6)3)).(3^(log_(6)3))`
`= 2.6^(log_(6)3)`
`=2.3^(log_(6)6)`
`=2xx3=6`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise JEE Previous Year|5 Videos

Similar Questions

Explore conceptually related problems

6^(log_6 5)+3^(log_9 16)=

Which of the following is the largest A)2^(log_5 6) B)3^(log_6 5) C)3^(log_5 6) D)3

If (2)^(log_(2)x^(2))-(3)^(log_(3)(x))-6=0 ,then sum of all possible values of x is

The value of the expression (1)/(log_(4)(18))+(1)/(2log_(6)(3)+log_(6)(2))+(2)/(log_(3)(18)')

In the equadratic equation A(sqrt3-sqrt2)x^2+B/(sqrt3+sqrt2) x+C=0 with alpha, beta as its roots. If A=(49+20sqrt6)^(1/4); B=sum of the infinite G.P as 8sqrt3+(8sqrt6)/sqrt3+(16)/sqrt3+.....oo and |alpha-beta|=(6sqrt6)^k where k=log_6 10-2 log_6 sqrt5+log_6 sqrt((log_6 18 + log_6 72)), then find the value of C.

A denotes the product xyz where x,y and z satisfy log_3 x= log5-log7 and log_5 y=log7-log 3 and log_7 z=log 3-log5 B denotes the sum of square of solution of the equation, log_2(log_2 x^6 - 3) - log_2(log_2 x^4 - 5) = log_2 3 C denotes characterstio of logarithm log_2 (log_2 3)-log_2 (log_4 3)+log_2(log_4 5)-log_2(log_6 5)+log_2 (log_6 7)-log_2 (log_6 3) The valuo of A+B+C is equal to

(log_(2)3)(log_(1/3)5)(log_(4)6)<1

let E=log_(2)(log_(2)3)+log_(2)(log_(3)4)+log_(2)(log_(4)5)+log_(2)(log_(5)6)+log_(2)(log_(6)7)+log_(2)(log_(7)8 then 8^(E) is

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

The expression (1)/(log_(5)3)+(1)/(log_(6)3)-(1)/(log_(10)3) simplifies to