Home
Class 12
MATHS
If a^(2) + b^(2) = 7 ab," prove that " ...

If `a^(2) + b^(2) = 7 ab," prove that " log((a+b)/3) = 1/2 (log a + log b)`.

Text Solution

Verified by Experts

`a^(2)+b^(2)= 7 ab`
` or (a+b)^(2) = 9 ab`
` or log(a+b)^(2) = log 9 ab`
` or 2 log(a+b) = 2log 3+log a+ log b`
` or 2(log(a+b)-log 3) = log a+ log b`
` or log((a+b)/3) =1/2 (log a+ log b)`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.4|12 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.5|13 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

If a^(2)+b^(2)=23ab, then prove that (log((a+b)))/(5)=(1)/(2)(log a+log b)

If a^(2)+b^(2)=7ab, prove that log((1)/(3)(a+b))=(1)/(2)(log a+log b)

If a^(2)+b^(2)=23ab, then prove that: (log(a+b))/(5)=(1)/(2)(log a+log b)

If a^(2) + b^(2) = 7 ab , then log (( a + b)/(3 )) equals

If a^(2)+b^(2)=23ab , then prove that log(a+b)/5=1/2(loga+logb)

If a^(2)+b^(2)=7ab prove that ((log(a+b))/(3))'=(log a+log b)/(2)

If a^(3)+b^(3)=ab(8-3a-3b) then prove that :log((a+b)/(2))=(1)/(3)(log a+log b)

If a^(2) + b^(2) = 7ab , then the vlaue of log [(1)/(3) (a + b)] is

If a^(2)+b^(2)=7ab then the value of is log((a+b)/(3))-(log a)/(2)-(log b)/(2)

log_(x)((a+b)/(2))=(1)/(2)(log a+log_(8)b)