What does a logarithmic function look like?

Question

Elijah Allen · Accepted Answer

The reflection of the exponential function on the axis #y=x# Logarithms are the inverse of an exponential function, so for #y=a^x#, the log function would be #y=log_ax#. So, the log function tell you what power #a# has to be raised to, to get #x#. Graph of #lnx#: graph{ln(x) [-10, 10, -5, 5]} Graph of #e^x#: graph{e^x [-10, 10, -5, 5]}

Elijah Allen · Answer

undefined A logarithmic function is a type of mathematical function that represents the inverse of an exponential function. It is written in the form f(x) = log_b(x), where "b" is the base of the logarithm. The most common bases are 10 (logarithm base 10, also known as the common logarithm) and e (logarithm base e, also known as the natural logarithm).

The graph of a logarithmic function typically looks like a curve that increases or decreases gradually depending on the base of the logarithm. If the base is greater than 1, the function increases slowly as x increases. If the base is between 0 and 1, the function decreases slowly as x increases.

For example, the graph of y = log(x) (logarithm base 10) starts at (1, 0) and increases slowly as x increases. As x approaches infinity, the function approaches positive infinity. Similarly, as x approaches 0 from the right side, the function approaches negative infinity.

On the other hand, the graph of y = ln(x) (natural logarithm base e) behaves similarly but has a different scale due to the different base. It also starts at (1, 0) and increases slowly as x increases, approaching positive infinity as x approaches infinity and approaching negative infinity as x approaches 0 from the right side.

In summary, logarithmic functions exhibit gradual growth or decay and have characteristic curves depending on the base of the logarithm.