...these numbers ; this would be a table of logarithms. We define the logarithm of a number therefore, the exponent of the power, to which it is necessary to raise a given or invariable number, in order to produce the proposed number. Thus in the equation a* = y, xk the...

...II. Of Exponential Quantities and Logarithms. 209. Resolution of the equation ax=b. The object of the question is, to find the exponent of the power to...number a, in order to produce another given number b. We will first consider some particular cases. Suppose it is required to resolve the equation 2r=64....

...numbers; we shall then have an idea of a table of logarithms. We generally call the logarithm of a number the exponent of the power to which it is necessary to raise a certain invariable number, in order to produce the first number. The invariable number may at first...

...all these numbers, an idea will be had of a table of logarithms. Hence, The logarithm of a number, is the exponent of the power to which it is necessary to raise a certain invariable number, in order to produce thefirst number. Any number, except 1, may be taken...

...treat it as an approximating fraction. Of Exponential Quantities. Resolution of the Equation a'—b. 255. The object of this question is, to find the exponent...number a, in order to produce another given number 6. Suppose it is required to resolve the equation 2*=64. By raising 2 to its different powers, we find...

...that of the dividend in order to obtain that of the quotient. , ,, n a1—'1 = — n Since I — I' is the exponent of the power to which it is necessary to raise a the base, in order to produce ~ it follows that I — f is the logarithm of ^ ie the logarithms of...

...multiplication, which is to add them together, we have Prom this last expression, it appears that I + I is the exponent of the power to which it is necessary to raise the base a, in order to produce the number nri. But nri is the product of n and n. Hence the logarithm...

...treat it as an approximating fraction. Of Exponential Quantities. Resolution of the Equation a'—b. 255. The object of this question is, to find the exponent...By raising 2 to its different powers, we find that 26=64 ; hence x—Q will satisfy the conditions of the equation. Again, let there be the equation 3*=243....

...treat it as an approximating fraction. • Of Exponential Quantities. Resolution of the Equation a*=b. 255. The object of this question is, to find the exponent...which it is necessary to raise a given number a, in ordef to produce another given number b. Suppose it is required to resolve the equation 2*=64. By raising...

...m=0, M will be equal to 1; if wi=l, M will be equal to 10, &.C. Hence, The logarithm of a number is the exponent of the power to which it is necessary to raise the base of the system in order to produce the number. 1 76. Letting, as before, a denote the base...