Answer
$x=6.5788$
Work Step by Step
The given expression can be written as:
$ (0.9)^x=0.5 $
We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ .
$ \log(0.9)^x=\log 0.5 $ and $ x \log (0.9)= \log 0.5 $
Now, we will evaluate the result for $x$.
$x=\dfrac{\log 0.5}{\log 0.9 }$
Therefore, our answer is: $x=6.5788$