Basic Math Examples

$100 = {(100)}^{2 z}$

Step 1

Rewrite the equation as $100^{2 z} = 100$ .

$100^{2 z} = 100$

Step 2

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

$100^{2 z} = 100^{1}$

Step 3

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

$2 z = 1$

Step 4

Divide each term in $2 z = 1$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 z = 1$ by $2$ .

$\frac{2 z}{2} = \frac{1}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 z}{2} = \frac{1}{2}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{1}{2}$

Decimal Form:

$z = 0.5$