Home
Class 11
MATHS
If a^(2) + b^(2) = 23ab, show that : "...

If `a^(2) + b^(2) = 23ab`, show that :
`"log" (a+b)/(5) = (1)/(2) (log a + log b)`.

Text Solution

Verified by Experts

`a^(2)+b^(2)=(a+b)^(2)-2ab = 23 ab`
`rArr (a+b)^(2)=25ab rArr a+b = 5sqrt(ab)` ……….(i)
LHS `=log(a+b)/5 = log(5sqrt(ab))/5 = 1/2logab = 1/2(loga +logb)`=RHS
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (JM)|8 Videos

Similar Questions

Explore conceptually related problems

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

Log(a^(2)-b^(2))=

If 9a^2 + 4b^2 = 18ab, then log (3a + 2b) =

Show that : log_(a)m div log_(ab)m = 1 + log_(a)b

If "log" (a-b)/(2) = (1)/(2) (log a + log b), show that : a^(2) + b^(2) = 6ab .

If a^(2) = log x, b^(3) = log y and (a^(2))/(2) - (b^(3))/(3) = log c , find c in terms of x and y.

Prove that : (i) (log a)^(2) - (log b)^(2) = log((a)/(b)).log(ab) (ii) If a log b + b log a - 1 = 0, then b^(a).a^(b) = 10

Statement-1: The solution set of the equation "log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x) 2 "is" {2^(-sqrt(2)), 2^(sqrt(2))}. Statement-2 : "log"_(b)a = (1)/("log"_(a)b) " and log"_(a) xy = "log"_(a) x + "log"_(a)y

if a^2+4b^2=12ab, then log(a+2b)

if a^2+4b^2=12ab, then log(a+2b)

ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
  1. Find the value of 2log2/5 +3 log25/8 -log 625/128

    Text Solution

    |

  2. If log(theta)x-log(theta)y= a, log(theta)y-log(theta)z=b and log(theta...

    Text Solution

    |

  3. If a^(2) + b^(2) = 23ab, show that : "log" (a+b)/(5) = (1)/(2) (log ...

    Text Solution

    |

  4. If log(a)x = p and log(b)x^(2) =q, then log(x)sqrt(ab) is equal to (wh...

    Text Solution

    |

  5. If a,b,c are distinct real number different from 1 such that (log(b)...

    Text Solution

    |

  6. Evaluate: 81^(1//log(5)3) + 27^(log(9)36) + 3^(4//log(l)9)

    Text Solution

    |

  7. Solve for x: a) log(0.5)(x^(2)-5x+6) ge -1, b) log(1//3)(log(4)(x^(2)-...

    Text Solution

    |

  8. Solve the following - (a)" " log(2)xle(2)/(log(2)x-1)" "

    Text Solution

    |

  9. Solve the equation: log(2x+3)x^(2) lt log(2x)(2x+3)

    Text Solution

    |

  10. Solve for x:2^(x+2) gt (1/4)^(1/x)

    Text Solution

    |

  11. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

    Text Solution

    |

  12. Show that log(4)18 is an irrational number.

    Text Solution

    |

  13. If in a right angled triangle, a and b are the lengths of sides and c ...

    Text Solution

    |

  14. If the arcs of same length in two circles subtend angles of 60^(@) and...

    Text Solution

    |

  15. If sintheta+sin^(2)theta=1, then prove that cos^(12)theta+3cos^(10)the...

    Text Solution

    |

  16. 4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)is equal to

    Text Solution

    |

  17. If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

    Text Solution

    |

  18. Prove that sqrt(3) " cosec "20^(@)-sec 20^(@)=4

    Text Solution

    |

  19. Prove that tan 70^(@)=cot70^(@)+2cot40^(@)

    Text Solution

    |

  20. If sin 2A=lambda sin 2B, prove that : (tan (A+B))/(tan(A-B)) = (lambda...

    Text Solution

    |