Domain And Range Of Exponential And Logarithmic Functions

Recall that the exponential function is defined as latex y b x latex for any real number x and constant latex b 0 latex latex b ne 1 latex where.

Domain and range of exponential and logarithmic functions. X 5 is your domain. 3 x 0 so the range would be y 4. The domain of y is latex left infty infty right latex.

Whatever base we have for the logarithmic function the range is always all real numbers for the base other than 10 we can define the range of a logarithmic function in the same way as explained above for base 10. However exponential functions and logarithm functions can be expressed in terms of any desired base b. However its range is such that y r.

In general the function y log b x where b x 0 and b 1 is a continuous and one to one function. The inverse of the exponential function y a x is x a y the logarithmic function y log a x is defined to be equivalent to the exponential equation x a y. X a y a 0 and a 1 it is called the logarithmic function with base a.

When evaluating a logarithmic function with a calculator you may have noticed that the only options are log 10 or log called the common logarithm or ln which is the natural logarithm. Calculus d 1 domain and range of exponential and logarithmic functions. Exponential functions have the general form y f x a x where a 0 a 1 and x is any real number.

Consider what the inverse of the. The range of log x is all real numbers so the range in this case is the real numbers. Remember that since the logarithmic function is the inverse of the exponential function the domain of logarithmic function is the range of exponential function and vice versa.

Y log a x only under the following conditions. The points 0 1 and 1 a always lie on the exponential function s graph while 1 0 and b 1 always lie on the logarithmic function s graph. Logarithmic functions are the inverses of exponential functions.