Is the graph of ${log (\frac{1}{2})}^{x}$ $log(1/2)^x$ always decreasing?

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Is the graph of ${log (\frac{1}{2})}^{x}$ $log(1/2)^x$ always decreasing?

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Answer 1 · 2016-09-20T08:27:42

This function is decreasing.

Explanation:

To find if the function is incresing, decreasing or constant you have to simplify it first.

$y = {log (\frac{1}{2})}^{x}$ $y=log(1/2)^x$

$y = {log (\frac{1}{2})}^{x} = x \times log (\frac{1}{2})$ $y=log(1/2)^x=x xx log(1/2)$

From this form we see that the function is linear and its slope is $log (\frac{1}{2})$ $log(1/2)$ . This number is negative, so the function is decreasing in all domain $RR$

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Is the graph of ${log (\frac{1}{2})}^{x}$ $log(1/2)^x$ always decreasing?

1 Answer

Explanation:

$y = {log (\frac{1}{2})}^{x}$ $y=log(1/2)^x$

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Is the graph of log(1/2)^xlog(12)xlog(1/2)^x always decreasing?

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Explanation:

y=log(1/2)^x y=log(12)xy=log(1/2)^x

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Is the graph of ${log (\frac{1}{2})}^{x}$ $log(1/2)^x$ always decreasing?

$y = {log (\frac{1}{2})}^{x}$ $y=log(1/2)^x$