Use the Definition of a Logarithm to Solve Logarithmic Equations $$\log _ { 6 } ( x - 1 ) = - 3$$

Multiple Choice

Use the Definition of a Logarithm to Solve Logarithmic Equations
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
- $$\log _ { 6 } ( x - 1 ) = - 3$$

A) $\left\{ \frac { 217 } { 216 } \right\}$
B) $\left\{ - \frac { 215 } { 216 } \right\}$
C) $\left\{ \frac { 217 } { 729 } \right\}$
D) $\left\{ - \frac { 215 } { 729 } \right\}$