Finite Math Examples

$15^{x} + 15 = 5^{x} \cdot 5 + 3^{x} \cdot 3$

Step 1

Simplify each term.

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Step 1.1

Multiply $5^{x}$ by $5$ .

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Step 1.1.1

Raise $5$ to the power of $1$ .

$15^{x} + 15 = 5^{x} \cdot 5^{1} + 3^{x} \cdot 3$

Step 1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15^{x} + 15 = 5^{x + 1} + 3^{x} \cdot 3$

Step 1.2

Multiply $3^{x}$ by $3$ .

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Step 1.2.1

Raise $3$ to the power of $1$ .

$15^{x} + 15 = 5^{x + 1} + 3^{x} \cdot 3^{1}$

Step 1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15^{x} + 15 = 5^{x + 1} + 3^{x + 1}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.68260619, 1.46497352$

Step 3