100=(100)2z

Rewrite the equation as (100)2z=100.

(100)2z=100

Create equivalent expressions in the equation that all have equal bases.

1002z=1001

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

2z=1

Divide each term in 2z=1 by 2.

2z2=12

Cancel the common factor of 2.

Cancel the common factor.

2z2=12

Divide z by 1.

z=12

z=12

z=12

The result can be shown in multiple forms.

Exact Form:

z=12

Decimal Form:

z=0.5

Solve for z 100=(100)^(2z)