Find the value of $\log_{5}(0.0016)$
$y=\log_{5}(0.0016)=\log_{5}(0.2)^4 \Rightarrow 5^y=(0.2)^4$
$\Rightarrow \log5^y=\log(0.2)^4$
$\Rightarrow y\log5=4\log(\dfrac{1}{5})$
$\Rightarrow y\log5=4(\log1-\log5)$
$\Rightarrow y\log5=-4\log5$
$\Rightarrow (y+4)\log5=0$
This is wrong, but I can't see where in my calculations I made a mistake. Thanks for the help.
Your working is fine and correct.
Here is a shorter working:
$$y=\log_5(0.2)^4=4\log_5(5^{-1})=-4$$