Can someone explain this to me? i don't understand how they got from what i labeled 1 to what is labeled 2. where did the 1/3 come from?

Step-by-step explanation:

Using exponent rules:

3^(n+1) = 3^(n) 3^(1)

So:

3^n / 3^(n+1)

= 3^n / (3^n × 3)

= 1 / 3

see attached

Step-by-step explanation:

see attached

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752