Kissing Curves

At exactly what values of a and x do the curves y = ax and y = loga(x) kiss?

Drag the slider value for a to explore this problem using the graph, then try to answer the questions that follow.

Note: use e for exp(1) in your responses to the questions below.

 

  
 

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Assessment

Hint: When entering mathematical expressions in the math boxes below, use the space key to step out of fractions, powers, etc. On Android, begin entry by pressing Enter.

Type simple mathematical expressions and equations as you would normally enter these: for example, "x^2[space]-4x+3", and "2/3[space]". For more interesting elements, use Latex notation (prefix commands such as "sqrt" and "nthroot3" with a backslash (\)): for example: "\sqrt(2)[space][space]". More?

 

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Steve Arnold 2018, Created with GeoGebra

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This dynamic figure was created using the latest version of the free GXWeb from Saltire Software, as shown below.

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©2018 Compass Learning Technologies ← Live Mathematics on the Web ← GeoGebra Showcase