Answer:
x = -2
Explanation:
Start:
216=6^(4x+11)
Use exponent property: (a^b*a^c)=a^(b+c)
Therefore:
216=6^(4x)*6^11
Simplify
216=(362797056)*6^(4x)
Divide
6^4x=(1/1679616)
Use exponent property: (a^b)^c = a^(b*c)
Therefore:
(6^4)^x=(1/1679616) OR (1296^x)=(1/1679616)
Use logarithms: log a b = c, where a^c=b
Therefore, log 1296 (1/1679616)=X
By logarithms property, log 1296 (1/1679616) = (log 10 (1/1679616))/(log 10 1296)
Use a calculator
x = -2