## Logarithms |

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4-place accurate amount angle between 84 Answers approximately base called Chapter characteristic colog column headed common logarithms compute cotangents decimal point denote diff difference directly dividing equivalent Examples explained exponent express find log sin Find the logarithms Find the values formulas fourth place functions of angles given logarithm greater half-way Hence horizontal line inclusive increase integral power interest interval last two figures less lies limit log arc log cos log csc log ctn log sec log sin ø log tan manner mantissa method of interpolation minute negative number whose logarithm obtained opposite place of decimals positive Proof quantity quotient reach reciprocal Referring root rule ſ log secant Show significant figure sine small table smaller type Solution star student subtracting successive logarithms tabular third division three figures true log units unity zero

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Side 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Side 4 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Side 7 - The integral part of a logarithm is called its characteristic, and the decimal part is called the mantissa.

Side 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».

Side 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.

Side 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

Side 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.

Side 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...

Side 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.