 | Levi Leonard Conant - 1909 - 183 σελίδες
...of the dividend minus the logarithm of the divisor. .'. log ~ — x — y — log m — log n. n 4. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. PROOF. mv = (10*)" = 10*y. .'. log mv = xy = y log... | |
 | Levi Leonard Conant - 1909 - 222 σελίδες
...logarithm of the dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log n. 4. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. PROOF. m? = (10*)" = 10*». .'. log m v = xy = y log... | |
 | Stimson Joseph Brown, Paul Capron - 1910 - 191 σελίδες
...Using the same quantities as in III, we have 2L = b * = b xv nb* or logs f-^-j = logs m - logs n. V. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power. Let m = b x , or logs m =• x; then m »= (6•)»... | |
 | Webster Wells, Walter Wilson Hart - 1912 - 424 σελίδες
...(a*)" = Ж», or a>" = J/p. .-. logM" = px. Therefore, . log M" = p log„ M. Rule. — In any system, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent indicating the power. ' EXAMPLE 1. Given log 7 = .8451, find... | |
 | Robert Edouard Moritz - 1913 - 453 σελίδες
...quantity which is to be raised to the nth power, nx is the logarithm of the resulting power; hence, The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index of the power to which it is to be raised, or If P = Nn, log P =... | |
 | Webster Wells, Walter Wilson Hart - 1913 - 285 σελίδες
...Also, (aIY — Mp, or ар1 = Мр. .: logM"=px. Therefore, log M"=p loga M. Rule. — In any system, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent indicating the power. EXAMPLE 1. Given log 7 = .8451, find log... | |
 | William Miller Barr - 1918
...difference will be the logarithm of the fraction. Involution by Logarithm. — On the principle that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power, we have the following rule. Multiply the logarithm of the number by the exponent... | |
 | Walter Burton Ford, Charles Ammerman - 1920 - 299 σελίδες
...the fourth. We then have 254, which means 25X25X25X25. This illustrates the following rule. RULE IX. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent indicating the power. Thus log 3.17" = 10 log 3.17; similarly,... | |
 | Walter Burton Ford - 1922 - 264 σελίδες
...= log 25+log 25+log 25+log 25, or log 254 = 4 log 25. This illustrates the following rule. RULE IX. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent indicating the power. Thus log 3.17i0 = 101og 3.17; similarly,... | |
 | Paul Carus - 1914
...to the logarithm of the numerator diminished by the logarithm of the denominator, the logarithm of a power of a number is equal to the logarithm of that number multiplied by the index, and the logarithm of the nth root of a number is equal to the logarithm of that number divided by n.... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
