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If a^2+b^2=23 a b , then prove that l...

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

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ALLEN-LOGARITHMS-All Questions
  1. If log5p=a and log2q=a , then prove that (p^4q^4)/(100)=100^(2a-1)

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  2. The value of 7log(16/15)+5log(25/24)+3log(81/80)=

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

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  4. If (log)a x=p\ a n d(log)b x^2=q ,\ t h e n(log)xsqrt(a b) is equal to...

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  5. If a, b, c are distinct positive real numbers each different from unit...

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  6. Evaluate: 81^(1//log(s)3) + 27^(log(g)36) + 3^(4//log(l)9)

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  7. If ||x-1|-2|=5 then find xdot

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  8. If |x-1|+|x+1|=2,\ then find\ xdot

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  9. Solve : x|x+3|+2|x+2|=0

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  10. Show that log4 (18) is an irrational number

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  11. If in a right angled triangle, a\ a n d\ b are the lengths of sides ...

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  12. If 6/5 a^A-3^B=9^C where A=loga x.log(10) aloga 5,B=log(10) (x/10) and...

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  13. Solve : (log)((2"x"-1))\ ((x^4+2)/(2x+1))\ =1

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  14. 1/((log)(sqrt(b c))a b c)+1/((log)(sqrt(c a))a b c)+1/((log)(sqrt(a b)...

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  15. The ratio (2^(log(2^(1/4))a)-3^(log(27)(a^2+1)^3)-2a)/(7^(4log(49)a-a-...

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  16. The value of expression, (log)4((x^2)/4)-2(log)4(4x^4) when x=-2 is -6...

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  17. Which one of the following denotes the greatest positive proper fra...

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  18. If p=s/((1+k)^n),\ t h e n\ n\ equals a.logs/(p(1+k)) b. (log(s//p))...

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  19. Value of x satifying (log)(10)sqrt(1+x)+3(log)(10)sqrt(1-x)=(log)(10)s...

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  20. The equation (log)2(2x^2)+(log)2xdotx^((log)x((log)2x+1))+1/2log4 2(x^...

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