Is #R(x)=4 ln(x)# an exponential function?

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Answer 1 · 2018-06-26T12:26:45

#color(blue)("No, it's a logarithmic function")#

#R(x)=4ln(x)# is a logarithmic function.

Logarithmic functions are the inverses of exponential functions.

If we rearrange #y=4ln(x)# to find #x# as a function of #y#

#y=4ln(x)#

#y/4=ln(x)#

#e^(y/4)=e^(ln(x))#

#e^(y/4)=x#

Substituting #x=y#

#y=e^(x/4)color(white)(88)# This is an exponential function.

So:

#y=e^(x/4)# is the inverse of the logarithmic function #y=4ln(x)#

Conversely: #y=4ln(x)# is the inverse of the exponential function #y=e^(x/4)#