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