Solve the equation $f ( x ) = g ( x )$ algebraically.
$$\begin{array} { c }
f ( x ) = \ln e ^ { 3 x - 9 } \
g ( x ) = x - 5
\end{array}$$
A) 0
B) $- 1$
C) 2
D) 5
E) 1

Question

Solve the equation $f ( x ) = g ( x )$ algebraically.
$$\begin{array} { c } 
f ( x ) = \ln e ^ { 3 x - 9 } \
g ( x ) = x - 5
\end{array}$$
A) 0
B) $- 1$
C) 2
D) 5
E) 1

Quizplus · Accepted Answer

The equation $f(x) = g(x)$ simplifies to $\ln e^{3x - 9} = x - 5$. The property of logarithms $\ln e^y = y$ simplifies the left side to $3x - 9$. Setting the equations equal gives $3x - 9 = x - 5$. Solving for $x$, we subtract $x$ from both sides and add $9$ to both sides to get $2x = 4$, which simplifies to $x = 2$.

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