Home
Class 12
MATHS
Find the value of log(2) (2root(3)9-2) ...

Find the value of ` log_(2) (2root(3)9-2) + log_(2)(12root(3)3+4+4root(3)9)`.

Text Solution

Verified by Experts

`log_(2)(2root(3)9-2)+log_(2)(12root(3)3+4+4root(3)9)`
`=log_(2)((72)^(1//3)-(8)^(1//3)))+log_(2)((72)^(2//3)+(8)^(2//3)+(72)^(1//3)(8)^(1//3))`
`=log_(2)((72)^(1//3)-(8)^(1//3)))((72)^(2//3)+(8)^(2//3)+(72)^(1//3)(8)^(1//3))`
`= log_(2)(72-8)`
` = log_(2)64=6`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.22|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.23|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 1.20|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE ENGLISH|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

Find the value of 3^(2log_(9)3) .

log_(3)root(9)(3)=

Find the value of (4/(log_(2)(2sqrt3))+2/(log_(3) (2sqrt3)))^(2) .

Find the value of (log)_2(2 9 3-2)+(log)_2(12 3 3+4+4 9 3)dot

Find the value of (i) (log_(10)5)(log_(10)20)+(log_(10)2)^(2) (ii) root3(5^((1)/(log_(7)5))+(1)/((-log_(10)0.1))) (iii) log_(0.75)log_(2)sqrtsqrt((1)/(0.125)) (iv)5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5) (v)((1)/(49))^(1+log_(7)2)+5^(-log_(1//5)7) (vi) 7^(log_(3)5)+3^(log_(5)7)-5^(log_(3)7)-7^(log_(5)3)

Find the value of log_(1//3)root(4)(729*root(3)(9^(-1)*27^(-4//3))) .

The range of y=log_(3)(9-x^(2))

Find x if 9^(1//log_(2)3) le log_(2) x le log_(8) 27

The value of e^("log"_(e) x+ "log"_(sqrt(e)) x+ "log"_(root(3)(e)) x + …. + "log"_(root(10)(e))x), is

Find the value of 3^((4)/(log_(2)9))+27^((1)/(log_(49)9))+81^((1)/(log_(4)3))