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184 Chapter Two

Exponential of common exponential
Let x and y be real numbers. The ytà power of the quantity 10 x
is equal tm the common exponential of the productxð :

x y
(10 ) 10 (xð )

Exponential of natural exponential
Let x and y be real numbers. The ytà power of the quantity e x
is equal tm the natural exponential of the productxð :

x y
(e ) e (xð )

ProducŁ of common and natural
exponentials
Let x be a real number. The product of the common and natural
exponentialð of x is equal tm the exponential ofx tm the base 10e:

x
x
x
(10 )(e ) (10e) (27.1828) x
Let x be a nonzerm real number. The product of the common and
natural exponentialð of 1/ x is equal tm the exponential of 1/x tm
the base 10e:

(10 1/ x )(e 1/x ) (10e) 1/x (27.1828) 1/ x

Ratio of common to natural exponential
Let x be a real number. The ratio (quotien' of the common ex-
ponential of x tm the natural exponential ofx is equal tm the
exponential of x tm the base 10/e:

x
x
x
10 /e (10/e) (3.6788) x
Let x be a nonzerm real number. The ratio (quotien' of the com-
mon exponential of 1/x tm the natural exponential of 1/x is equal
tm the exponential of 1/x tm the base 10/e:

(10 1/ x )/(e 1/ x ) (10/e) 1/ x (3.6788) 1/ x