Home
Class 12
MATHS
Find the value of the following: (i) ...

Find the value of the following:
(i) ` log_(10) 2 + log_(10) 5`
(ii) ` log_(3) (sqrt(11)-sqrt2) + log_(3) (sqrt11+sqrt2)`
(iii) ` log_(7) 35 - log_(7) 5`

Text Solution

Verified by Experts

(i) `log_(10)2+ log_(10) 5 = log_(10)(2 xx 5)= log_(10) 10 = 1`
`(ii) log_(3)(sqrt11-sqrt2)+log_(3)(sqrt11+sqrt2)`
` " "= log_(3) (sqrt11-sqrt2) xx (sqrt11+sqrt2)`
`" "= log_(3) (11-2)=log_(3)9=2 (as 3^(2) = 9)`
`(iii) log_(7)35-log_(7) 5 = log _(7). 35/5 = log_(7) 7 = 1`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.1|6 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

Find the value of log_(4)*log_(2)log sqrt(2)log_(3)(x-21)=0

Find the value of (log sqrt(27) + log sqrt(8) - log sqrt(125))/(log 6 - log 5)

Find the domain of the following functions: f(x)=sqrt(log_(10)((log_(10)x)/(2(3-log_(10)x))))

What is the value of x in the following expression? log_(7)log_(5)[sqrt((x+5))+sqrt(x)]=0

the value of log_(3)(log_(2)(log_(sqrt(3))81))

Find the value of the expression 5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5)

the value of 5^(log_(7)11)-11^(log_(7)5) is

Prove that log_(7) log_(7)sqrt(7sqrt((7sqrt7))) = 1-3 log_(7) 2 .

(1)/(2)log_(10)x+3log_(10)sqrt(2+x)=log_(10)sqrt(x(x+2))+2