CUBIC AND HIGHER EQUATIONS, 



377 



l^OTE 4. The same rule also, among other more dlffi- 

 €ult forms of equations, succeeds very well in what are 

 called exponential equations^ or those, which have an un- 

 known quantity for the exponent of the power ; as in the 

 following example. 



4. To find the value of x m the exponential equation 



ft;*zzioo. 



For the more easy resolution of this kind of equations, 

 it is convenient to take the logarithms of them, and then 

 compute the terms by means of a table of logarithm.s. 

 Thus, the logarithms of the two sides of the present equation 

 are, ^X log. of xzni^ the log. of 100. Then by a few 

 trials it is soon perceived, that the value of x is somewhere 

 between the two numbers 3 and, 4, and indeed nearly in 

 the middle between them, but rather nearer the latter than 

 the former. By taking therefore first xzzzy^y and then 

 a:z=:3'6, and working with the logarithms, the operation 

 ^ill be as follows : 



First, suppose ►Yzz 3*5. 

 Logarithm of 3*5 zz 0*5440680 



Then 3*5 X log- 3*5 = 1-904238 



The true number 2*000000 



— '095762 

 4-'oo2689 



•098451 sum of the errors. Then, 

 Z z , 



As 



