Logarithmic Functions - Maple Programming Help

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Logarithmic Functions

 Logarithms with integer bases Let $n>1$ be an integer. The function ${\mathrm{log}}_{n}\left(x\right)$, which is read the "logarithm (base $n$) of $x$" or the "base $n$ logarithm of $x$" is the inverse of the function $f\left(x\right)={n}^{x}$. Thus, $b={n}^{a}$ exactly when $a={\mathrm{log}}_{n}\left(b\right)$. The domain of ${\mathrm{log}}_{n}\left(x\right)$ is the set of positive numbers. The range of ${\mathrm{log}}_{n}\left(x\right)$ is all numbers. A logarithm is an exponent: ${\mathrm{log}}_{n}\left(b\right)$ is the power to which you raise $n$ to obtain the value $b$. Mathematically, ${n}^{{\mathrm{log}}_{n}\left(b\right)}=b$.

Explore how

Use the slider below the graph to change the values of $b$.  Explore the graphs of the logarithmic function  and its corresponding exponential function $y={b}^{x}$ as you vary the integer $b$ from 2 to 10.

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