We have to apply the change of base formula:
[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]
We can apply this to our expression as:
[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]
Answer: -4.6
