1. Solve: log (y-1) = -log(y-9)

2. Find the inverse of the logarithmic function f defined by f(y)= 2log5 (2y-8)+3.

1 answer

log(y-1)=-log(y-9)
using the property of logarithms,
log(x) = -log(1/x), then
log(y-1)=log(1/(y-9))
take anti-log on both sides,

y-1 = 1/(y-9)
then solve for quadratic in y after cross-multiplication.