Complete Secondary AlgebraFisher and Schwatt, 1901 - 288 páginas |
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Página 412
... base b . = Ng E.g. , since 28 , 3 is the logarithm of 8 to the base 2 ; since 102 = 100 , 2 is the logarithm of 100 to the base 10 . The Logarithm of a given number n to a given base b is , there- fore , the exponent of the power to ...
... base b . = Ng E.g. , since 28 , 3 is the logarithm of 8 to the base 2 ; since 102 = 100 , 2 is the logarithm of 100 to the base 10 . The Logarithm of a given number n to a given base b is , there- fore , the exponent of the power to ...
Página 413
... base 2 ; as 4 = 22 , 8 = 23 , 16 = 24 , etc. Since , also , all the numbers intermediate between those given above ... base form what is called a System of Logarithms . The base is then called the base of the system . It follows from Art ...
... base 2 ; as 4 = 22 , 8 = 23 , 16 = 24 , etc. Since , also , all the numbers intermediate between those given above ... base form what is called a System of Logarithms . The base is then called the base of the system . It follows from Art ...
Página 414
... base 2 ? Since 2048 32.64 , we have - log , 2048 log , 32+ log , 64 = 5 + 6 = 11 = 7. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor ; or , log 。( m ÷ n ) = log1 m — logn ...
... base 2 ? Since 2048 32.64 , we have - log , 2048 log , 32+ log , 64 = 5 + 6 = 11 = 7. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor ; or , log 。( m ÷ n ) = log1 m — logn ...
Página 416
... base 10 : 14. log 50 . 15 . log 6 . 16. log 8 . 17. log 9 . 18. log 12 . 19 . log 36 . 20. log 108 . 21. log 4 . 22 ... base is 10. This system was intro- duced , in 1615 , by the Englishman , Henry Briggs . Logarithms to the base 10 are ...
... base 10 : 14. log 50 . 15 . log 6 . 16. log 8 . 17. log 9 . 18. log 12 . 19 . log 36 . 20. log 108 . 21. log 4 . 22 ... base is 10. This system was intro- duced , in 1615 , by the Englishman , Henry Briggs . Logarithms to the base 10 are ...
Página 417
... base 10 is also the base of our decimal system of numeration . The logarithms of most numbers are irrational , and thus approximate values are used . Properties of Common Logarithms . 13. In the following articles the subscript denoting ...
... base 10 is also the base of our decimal system of numeration . The logarithms of most numbers are irrational , and thus approximate values are used . Properties of Common Logarithms . 13. In the following articles the subscript denoting ...
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Términos y frases comunes
a₁ arithmetical means arithmetical progression assume b₁ b₂ coefficient column common logarithms continued fraction convergent series corresponding d₁ d₂ decimal places denominator depressed equation determinant digits divergent series Dividing elements equal equation whose roots EXERCISES expansion factor figure Find the value finite number Form the equation geometrical means geometrical progression given equation given series graph harmonical mean Hence increases indefinitely infinite series last term less limit logarithms mantissa method multiplying nth term number of combinations obtained partial fractions partial quotient permutations preceding article principle quadratic equation r₁ r₂ ratio real roots reciprocal equation result root of f(x S₁ second member series is convergent solution Solve the equation Sturm's Theorem Substituting subtracted transformed equation u₁ U₂ unknown number variable variations of sign whence wherein x-axis
Pasajes populares
Página 415 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 354 - C„.r. That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 351 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Página 313 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 317 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 310 - Two workmen can do a piece of work in 6 days. How long will it take each of them to do the work, if it takes one 5 days longer than the other ? 19.
Página 360 - V(a2 — °^)> etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 315 - In any proportion the terms are in proportion by. Composition ; that is, the sum of the first two terms is to the first term, as the sum of the last two terms is to the third ter.n.
Página 323 - If a body falls 256 feet in 4 seconds, how far will it fall in 10 seconds?
Página 373 - An infinite series is said to be divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great.