log16(216)

Rewrite as an equation.

log16(216)=x

Rewrite log16(216)=x in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then logb(x)=y is equivalent to by=x.

(16)x=216

Create expressions in the equation that all have equal bases.

(6-1)x=63

Rewrite (6-1)x as 6-x.

6-x=63

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

-x=3

Solve for x.

x=-3

The variable x is equal to -3.

-3

Evaluate log base 1/6 of 216