577. The Arithmetical Complement of a logarithm, or, briefly, the Cologarithm of the number, is the logarithm of the reciprocal of that number. Thus the colog 225 = log = log 1 — log 225. Since log 1 = 0, it may be written in the form 10-10 and then subtract log 225, RULE. 107.647817 · 10 To find the cologarithm of a number, subtract the loga rithm of the number from 10 and write 10 after the result. 578. The advantage gained by the use of cologarithms is the substitution of addition for subtraction. EXAMPLE. Find by the use of logarithms the value of 5.37 6 87X.079 EXERCISE LXXXVII Calculate the value of the following expressions by aid of logarithms: 40. (-8.5768)-0.4. 41. (-7.05873)-22. 42. (0.637803)0.65. 29 • 3 30. '318 0.045) 71 751 93 518 Find the value of the following logarithms: 55. log (abac + bc), if log a = log c = 0.49832. 0.75643, log b = 0.87254, Ans. 1.92440. 56. log Va+b2, if log a = 0.78241, log b = 0.63575. Ans. 57. log Vab, if log a 2.87655, log b = 2.79287. = Ans. 58. log (ab), if log a = 1.28643, log b = 0.85794. 0.87174. 2.62898. Ans. 1.81746. 59. logh (a + b + √ ab), if log h= 0.87432, log a log b = 0.36954. Ans. 1.29956. = Ans. 4.67237. 60. logh (2 + p2 + rp), if log h= 0.87456, log 0.49715, logr 1.75846, log p = 1.48763. = EXPONENTIAL EQUATIONS 579. An Exponential Equation is one in which the unknown quantity appears as an exponent. Certain equations of this character can be solved by taking the logarithms of both members, which gives an equation of the first degree that can be solved by the usual methods. Thus: [2558] can be found by logarithms or by |