Hi guys hope your weekend is going great! 
Now if you can check these problems and offer me some tips, you can make mine.
2)\(\displaystyle \L \;log_{\frac{1}{8}}\frac{1}{16}\,=\,x\)
I've tried putting it into exponential form, getting:\(\displaystyle \L \;(\frac{1}{2^3})^{x}\,=\,\frac{1}{2^4}\)
So I solved\(\displaystyle \L \;3x\,=\,4\,to\,x\,=\,\frac{4}{3}\) but it don't work.
3) \(\displaystyle \L \;M\,=\,\frac{2}{3}\,log\frac{E}{10^{11.8}}\)
M = 6.6, Find E:\(\displaystyle \L \;6.6\,=\,\frac{2}{3}\,log\frac{E}{10^{11.8}}\)
Multiply be 3/2:\(\displaystyle \L \;9.9\,=\,log\frac{E}{10^{11.8}}\)
Raise to the 10 base:\(\displaystyle \L \;10^{9.9}\,=\,\frac{E}{10^{11.8}}\)
\(\displaystyle \L \;E\,=\,10^{21.7}\)
4) Same formula, E = 3.98 x 10<sup>22</sup>, solve for M:\(\displaystyle \L \;M\,=\,\frac{2}{3}\,log\frac{3.98\,\cdot\,10^{21.7}}{10^{11.8}}\)
With my calc I got \(\displaystyle \L \;M\,\approx\,7.2\)
Now if you can check these problems and offer me some tips, you can make mine.
2)\(\displaystyle \L \;log_{\frac{1}{8}}\frac{1}{16}\,=\,x\)
I've tried putting it into exponential form, getting:\(\displaystyle \L \;(\frac{1}{2^3})^{x}\,=\,\frac{1}{2^4}\)
So I solved\(\displaystyle \L \;3x\,=\,4\,to\,x\,=\,\frac{4}{3}\) but it don't work.
3) \(\displaystyle \L \;M\,=\,\frac{2}{3}\,log\frac{E}{10^{11.8}}\)
M = 6.6, Find E:\(\displaystyle \L \;6.6\,=\,\frac{2}{3}\,log\frac{E}{10^{11.8}}\)
Multiply be 3/2:\(\displaystyle \L \;9.9\,=\,log\frac{E}{10^{11.8}}\)
Raise to the 10 base:\(\displaystyle \L \;10^{9.9}\,=\,\frac{E}{10^{11.8}}\)
\(\displaystyle \L \;E\,=\,10^{21.7}\)
4) Same formula, E = 3.98 x 10<sup>22</sup>, solve for M:\(\displaystyle \L \;M\,=\,\frac{2}{3}\,log\frac{3.98\,\cdot\,10^{21.7}}{10^{11.8}}\)
With my calc I got \(\displaystyle \L \;M\,\approx\,7.2\)
