Basic Math Examples

$\log_{3} (n) + \log_{9} (n) = 4 \frac{1}{2}$

Step 1

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\log_{3} (n) + \log_{9} (n) = 4 + \frac{1}{2}$

Step 1.2

Add $4$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\log_{3} (n) + \log_{9} (n) = 4 \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.2.2

Combine $4$ and $\frac{2}{2}$ .

$\log_{3} (n) + \log_{9} (n) = \frac{4 \cdot 2}{2} + \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\log_{3} (n) + \log_{9} (n) = \frac{4 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $2$ .

$\log_{3} (n) + \log_{9} (n) = \frac{8 + 1}{2}$

Step 1.2.4.2

Add $8$ and $1$ .

$\log_{3} (n) + \log_{9} (n) = \frac{9}{2}$

Step 2

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

$n \approx 27$

Step 3