Question

Solve the exponential equation for x 216 = 6^(4x+11)

Answer 1

Answer:

x = -2

Step-by-step 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