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

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