Question

1. \\(\ln e^{-6}\\)\

a) -6\
b) -2\
c) 6\
d) 1\

1. \\(\log_{2} 2^{4}\\)\

a) 4\
b) 2\
c) 1\
d) 16\

1. \\(\log_{10} (0.0001)\\)\

a) -5\
b) -3\
c) -4\
d) 3\

1. \\(\log_{10} (0.000001)\\)\

a) -3\
b) 5\
c) -7\
d) -6\

1. find the corresponding graph of \\(\log_{3} (x - 1) + 4\\)\

a) graph\
b) graph\
c) graph\
d) graph

Explanation:

Step1: Apply log identity $\ln e^x = x$

$\ln e^{-6} = -6$

Step2: Apply log identity $\log_b b^x = x$

$\log_2 2^4 = 4$

Step3: Rewrite 0.0001 as $10^{-4}$

$\log_{10}(10^{-4}) = -4$

Step4: Rewrite 0.000001 as $10^{-6}$

$\log_{10}(10^{-6}) = -6$

Step5: Analyze $\log_3(x-1)+4$ shift

Vertical asymptote at $x=1$, shifted up 4. Check graph a (asymptote $x=1$, passes near $(2,4)$ since $\log_3(1)+4=4$).

Answer:

1. a) -6
2. a) 4
3. c) -4
4. d) -6
5. a) [Graph a]