Home
Class 12
MATHS
If loge((a+b)/2)=1/2(loge a+loge b), the...

If `log_e((a+b)/2)=1/2(log_e a+log_e b),` then find the relation between `a and b dot`

Text Solution

Verified by Experts

`log_(e)((a+b)/2)= 1/2 (log_(e)a+log_(e) b)`
` = 1/2 (log_(e)ab) = (log_(e)sqrt(ab))`
` rArr (a+b)/2 = sqrt(ab)`
` or a+b-2sqrt(ab) = 0`
` or (sqrta-sqrtb)^(2)= 0`
`or a = b`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.24|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.25|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.22|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

If log_(b) n = 2 and log_(n) 2b = 2 , then find the value of b.

If log_(e)2.log_(x)25 = log_(10)16.log_(e )10 , then find the value of x.

If log_(a)b=10 and log_(6a)(32b)=5 find the value of a

If log_(e)(x^(2)-16)lelog_(e)(4x-11) ,then-

If a=(log)_(12)18 , b=(log)_(24)54 , then find the value of a b+5(a-b)dot

The value of (6 a^(log_(e)b)(log_(a^(2))b)(log_(b^(2))a))/(e^(log_(e)a*log_(e)b)) is (a) independent of a (b) independent of b (c) dependent on a (d) dependent on b

If log_(a)b=2, log_(b)c=2, and log_(3) c= 3 + log_(3) a,then the value of c/(ab)is ________.

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

"If "log_(e)(log_(e) x-log_(e)y)=e^(x^(2_(y)))(1-log_(e)x)," then find the value of "y'(e).

If f(x)=log_(x)(log_(e)x) , then the value of f'(e ) is -

CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-ILLUSTRATION 1.23
  1. If loge((a+b)/2)=1/2(loge a+loge b), then find the relation between a ...

    Text Solution

    |