Ok first of all, I EXTREMELY appreciate your use of parenthesis. Ok so first just raise both sides to the power of 1/2.
[tex](\frac{3}{8})^{x}=\frac{8}{11}[/tex]
You'll see why I didn't include a negative. Then apply the log base 3/8 and you get
[tex]x = log_{ \frac{3}{8} }( \frac{8}{11} ) [/tex]
Then you split the log up and you get
[tex]x = log_{ \frac{3}{8} }(8) - log_{ \frac{3}{8} }(11) [/tex]
You couldn't put a negative value for a log. That is why I excluded the negative part of the sqrt.
