LogarithmsCharles W. Sever, 1882 - 43 páginas |
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Página 1
... exponent de- noting the power to which a fixed number called the base must be raised in order to produce N. Thus , if N = b " , then is log , N = x ; or , in words , when the base is b the logarithm of N is x . ... log , 8 = 3 . 1 = 4 ...
... exponent de- noting the power to which a fixed number called the base must be raised in order to produce N. Thus , if N = b " , then is log , N = x ; or , in words , when the base is b the logarithm of N is x . ... log , 8 = 3 . 1 = 4 ...
Página 4
... exponent of the power . Proof : If l = b2 , then is log , l = x , lm = ( bx ) m = bmx ; log 7m = mx = mx logl . Under this head may be brought a root , for a root may be regarded as a fractional power . 1 = 1 x 2x m = bm ; .log Im X 1 x ...
... exponent of the power . Proof : If l = b2 , then is log , l = x , lm = ( bx ) m = bmx ; log 7m = mx = mx logl . Under this head may be brought a root , for a root may be regarded as a fractional power . 1 = 1 x 2x m = bm ; .log Im X 1 x ...
Página 7
... ( exponent ) by an integer . § 11. The integral part of a logarithm is called its characteristic , and the decimal part its mantissa . The characteristic , when the number is not an integral power of 10 , may be found easily by noting ...
... ( exponent ) by an integer . § 11. The integral part of a logarithm is called its characteristic , and the decimal part its mantissa . The characteristic , when the number is not an integral power of 10 , may be found easily by noting ...
Página 18
... exponent of the root ; i.e. , in this example , 5 tens , or 50 . 5. Find the cube root of 0.27 . log 0.271.4314 ; increasing the characteristic −1 by 3 tens , or 30 , we get log 0.27 ..log = 29.4314 — 30 ; 0.27 = 9.8105 - 10 = 1.8105 ...
... exponent of the root ; i.e. , in this example , 5 tens , or 50 . 5. Find the cube root of 0.27 . log 0.271.4314 ; increasing the characteristic −1 by 3 tens , or 30 , we get log 0.27 ..log = 29.4314 — 30 ; 0.27 = 9.8105 - 10 = 1.8105 ...
Página 20
... exponent which will produce a negative number , since 10 with any exponent ( positive or negative ) gives always a pos- itive quantity , greater than unity if the exponent is positive , and between zero and unity if the exponent is ...
... exponent which will produce a negative number , since 10 with any exponent ( positive or negative ) gives always a pos- itive quantity , greater than unity if the exponent is positive , and between zero and unity if the exponent is ...
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Términos y frases comunes
103 opposite 4-place 7-place table amount angle between 84 Answers arco arithm arithmetical complement column headed common logarithms cosecant cotangents of angles decimal point diff division of page Examples exponent find an angle find log sec find log sin Find the logarithms Find the numbers Find the values found with definiteness fourth place FRANCIS PEABODY MAGOUN full-faced type functions of angles given logarithm horizontal line inclusive integral power know from Trigonometry last two figures Let us find log arc 1'-e log cos log csc log ctn log log log tan log logarithm is base logarithms of numbers mantissa method of interpolation number is equal number whose logarithm obtained place of decimals printed in full-faced secant significant figure sines and cosines small table smaller type successive logarithms system of logarithms system the logarithm tabular log third division three figures tracting the latter trigono TRIGONOMETRIC FUNCTIONS true log
Pasajes populares
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 4 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 7 - The integral part of a logarithm is called its characteristic, and the decimal part is called the mantissa.
Página 3 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a».
Página 1 - The exponent of the power to which a fixed number called the Base must be raised in order to produce a given number is called the Logarithm of the given number.
Página 2 - IV. The logarithm of a root of a number is found by dividing the logarithm of the number by the index of the root : log v/a = (log a)/b. This follows from the fact that if 10
Página 6 - Art. 66 we see that the logarithm of a number which is not an integral power of 10 is an integer plus a decimal.
Página 27 - ... cosines, &c., themselves. When logarithms were invented they were called artificial numbers, and the originals for which logarithms were computed, were accordingly called natural numbers. Thus, in speaking of a table of sines, to express that it is not the logarithms of the sines which are given, but...
Página 15 - For example, to obtain 1000, three tens must be multiplied together so that the logarithm of 1000 is 3. The logarithm of the reciprocal of a number is equal to the negative of the logarithm of the number.