How do you graph $y = {log}_{\frac{1}{2}} x$ $y=log_(1/2)x$ ?

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Answer 1 · 2017-01-13T07:27:10

The standard graph of $ln x$ $lnx$ scaled by: $- \frac{1}{ln 2}$ $-1/ln2$

Remember: ${log}_{b} a = \frac{ln a}{ln b}$ $log_b a = lna/lnb$

In our example: $y = {log}_{\frac{1}{2}} x$ $y= log_(1/2) x$

Hence: $y = \frac{ln x}{ln (\frac{1}{2})} = ln x \cdot - \frac{1}{ln 2}$ $y = lnx/ln(1/2) = lnx * -1/ln2$

Thus:
The graph of $y$ $y$ is the standard graph of $ln x$ $lnx$ scaled by: $- \frac{1}{ln 2}$ $-1/ln2$

The graph of $y$ $y$ is shown below:

graph{ lnx * -1/ln2 [-2.114, 15.666, -4.47, 4.42]}

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