Basic Math Examples

$81 = 3^{z - 3}$

Step 1

Rewrite the equation as $3^{z - 3} = 81$ .

$3^{z - 3} = 81$

Step 2

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

$3^{z - 3} = 3^{4}$

Step 3

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

$z - 3 = 4$

Step 4

Move all terms not containing $z$ to the right side of the equation.

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Step 4.1

Add $3$ to both sides of the equation.

$z = 4 + 3$

Step 4.2

Add $4$ and $3$ .

$z = 7$