Template:Math/testcases

This page is for testing in the Cologne Blue, Modern, Monobook and Vector skins. Sans-serif / serif scaling ratio is 118%.

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Times New Roman (current template)

 * (font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif;)

A compact way of rephrasing the point that the base-$b$ logarithm of $y$ is the solution $x$ to the equation $f(x) = b^{x} = y$ is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line $x = y$, as shown at the right: a point $(t, u = b^{t})$ on the graph of the exponential function yields a point $(u, t = log_{b}u)$ on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function $f(x) = b^{x}$ is continuous and differentiable, so is its inverse function, $log_{b}(x)$. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

Computer Modern Unicode, Times New Roman (/sandbox1)

 * (font-family: 'CMU Serif', 'Times New Roman', 'Nimbus Roman No9 L', Times, serif;)

A compact way of rephrasing the point that the base- logarithm of is the solution  to the equation  is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line, as shown at the right: a point on the graph of the exponential function yields a point  on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function is continuous and differentiable, so is its inverse function,. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

Palatino Linotype (/sandbox2)

 * (font-family: 'Palatino Linotype', 'URW Palladio L', Palatino, serif;)

A compact way of rephrasing the point that the base- logarithm of is the solution  to the equation  is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line, as shown at the right: a point on the graph of the exponential function yields a point  on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function is continuous and differentiable, so is its inverse function,. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

Century Schoolbook (/sandbox3)

 * (font-family: 'Century Schoolbook', 'Century Schoolbook L', serif;)

A compact way of rephrasing the point that the base- logarithm of is the solution  to the equation  is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line, as shown at the right: a point on the graph of the exponential function yields a point  on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function is continuous and differentiable, so is its inverse function,. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

Cambria (/sandbox4)

 * (font-family: Cambria, serif;)

A compact way of rephrasing the point that the base- logarithm of is the solution  to the equation  is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line, as shown at the right: a point on the graph of the exponential function yields a point  on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function is continuous and differentiable, so is its inverse function,. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

Constantia (/sandbox5)

 * (font-family: Constantia, serif)

A compact way of rephrasing the point that the base- logarithm of is the solution  to the equation  is to say that the logarithm function is the inverse function of the exponential function. Inverse functions are closely related to the original functions: the graphs of the two correspond to each other upon reflecting them at the diagonal line, as shown at the right: a point on the graph of the exponential function yields a point  on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function is continuous and differentiable, so is its inverse function,. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".