Question

9^(-x+9)= 11^(-5x) solve for x.

Answer 1

\[\ln 9^{(-x+9)}=\ln 11^{(-5x)}\]
\[(-x+9) \ln9=-5x \ln11\]
\[-x*\ln9+9*\ln9=-5x*\ln11\]
get x's together
\[-x*\ln9+5x*\ln11=-9 \ln9\]
\[x(-\ln9+5\ln11)=-9\ln9\]
get x by itself by dividing by -ln9+5ln11

Answer 2

\[x=\frac{-9\ln9}{5\ln11-\ln9}\]

Answer 3

would it be the same answer if we put \[9\log (9)\div \log (9) - 5\log (9)\] ??

Answer 4

no
you could write
\[x=\frac{9\ln9}{\ln9-5\ln11}\]

Answer 5

is that what you meant?