Mathematics, 18.07.2019 16:00 samiiegarciia
The function f(x)=log0.75^x is decreasing. true or false
Answers: 1
![f(x)=log(.75^x)=log[ (\frac{3}{4}) ^{x}]=log( \frac{3^x}{4^x})](/tpl/images/0104/5818/61f34.png)
the function is increasing, if 
the function is decreasing.![\frac{d}{dx}[log( \frac{3^x}{4^x})]= \frac{4^x}{3^x}[ \frac{d}{dx} (\frac{3^x}{4^x})]=\frac{4^x}{3^x} \frac{4^x[ \frac{d}{dx} (3^x)]-3^x[ \frac{d}{dx} (4^x)]}{ 4^2^x}=](/tpl/images/0104/5818/bf297.png)
![\frac{4^x}{3^x} \frac{4^x[3^xlog(3)]-3^x[4^x[4^xlog(4)]}{ 4^2^x}=log(3)-log(4)\ \textless \ 0](/tpl/images/0104/5818/f829b.png)
and 
such that 
, then if 
the function is increasing and if 
the function is decreasing. You can verify the function is decreasing with any two numbers in the function's domain.
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The function f(x)=log0.75^x is decreasing. true or false...
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