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Exponential Functions for Physics Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 17, 2011

Ratio Of Common To Natural Exponential

Let x be a real number. The ratio (quotient) of the common exponential of x to the natural exponential of x is equal to the exponential of x to the base 10/ e :

10 x / e x = (10/ e ) x ≈ (3.6788) x

Now suppose that x is some nonzero real number. The ratio (quotient) of the common exponential of 1/ x to the natural exponential of 1/ x is equal to the exponential of 1/ x to the base 10/ e :

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

Ratio Of Natural To Common Exponential

Let x be a real number. The ratio (quotient) of the natural exponential of x to the common exponential of x is equal to the exponential of x to the base e /10. That is to say:

e x /10 x = ( e /10) x ≈ (0.271828) x

Now suppose that x is some nonzero real number. The ratio (quotient) of the natural exponential of 1/ x to the common exponential of 1/ x is equal to the exponential of 1/ x to the base e /10:

( e 1/ x )/(10 1/ x ) = ( e /10) 1/ x ≈ (0.271828) 1/ x

Common Exponential Of Ratio

Let x and y be real numbers, with the restriction that y ≠ 0. The common exponential of the ratio (quotient) of x to y is equal to the exponential of 1/ y to the base 10 x :

10 x/y = (10 x ) 1/ y

A similar situation exists for base e . The natural exponential of the ratio (quotient) of x to y is equal to the exponential of 1/ y to the base e x :

e x/y = ( e x ) 1/ y

Practice problems for these concepts can be found at:  Logarithms, Exponentials, And Trigonometry for Physics Practice Test

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