지수함수 극한

$\displaystyle \lim\limits _{x \rightarrow 0} \frac{( a + 12 ) ^{x} - a ^{x}}{x}$ $\displaystyle = \lim\limits _{x \rightarrow 0} \frac{\{ ( a + 12 ) ^{x} - 1 \} - \{ a ^{x} - 1 \}}{x}$ $= \ln ( a + 12 ) - \ln a$ $\displaystyle = \ln \frac{a + 12}{a} = \ln 3$ $\displaystyle \therefore \frac{a + 12}{a} = 3$ $a + 12 = 3 a$ $\therefore a = 6$