domain of log function

domain of log function To find the domain of a function consider any restrictions on the input values that would make the function undefined including dividing by zero taking the square root of a negative number or taking the logarithm of a negative number

Identify the domain of a logarithmic function Before working with graphs we will take a look at the domain the set of input values for which the logarithmic function is defined Recall that the exponential function is defined as displaystyle y b x y bx for any real number x and constant displaystyle b 0 b 0 displaystyle b ne 1 In this section you will learn how to find domain and range of logarithmic functions The table shown below gives the domain and range of different logarithmic functions Name of the Parts of a Logarithm

domain of log function

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domain of log function
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Definition Domain of the Logarithmic Function The domain of the logarithmic function is x x 0 x x 0 or 0 0 i e the value or argument of the logarithm is always positive Steps for obtaining the domain of logarithmic function Here are some examples of logarithmic functions f x log 5 x g x log 3x 1 h x ln 4x 2 Finding Domain and Range The domain of the function y log b x is x 0 or 0 and the range of any logarithmic function is the set of real numbers Let us determine the domain of the logarithmic function g x log 3x 1

Identify the domain of a logarithmic function Before working with graphs we will take a look at the domain the set of input values for which the logarithmic function is defined 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 The domain of the function is x gt 0 or 0 infty in interval notation The range of the function is all real numbers or infty infty in interval notation

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The function y log 2 x has the domain of set of positive real numbers and the range of set of 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 In general the logarithmic function always has positive x and never crosses the y axis always intersects the x axis at x 1 in other words it passes through 1 0 equals 1 when x a in other words it passes through a 1 is an Injective one to one function Its Domain is the Positive Real Numbers 0 Its Range is the Real Numbers

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