Finite Math Examples

$8^{y} = 4^{2 x + 3}$

Step 1

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

$2^{3 y} = 2^{2 (2 x + 3)}$

Step 2

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

$3 y = 2 (2 x + 3)$

Step 3

Divide each term in $3 y = 2 (2 x + 3)$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 y = 2 (2 x + 3)$ by $3$ .

$\frac{3 y}{3} = \frac{2 (2 x + 3)}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{2 (2 x + 3)}{3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 (2 x + 3)}{3}$