Algebra Examples

$\log_{6} (x) + \log_{6} (9) = \log_{6} (54)$

Step 1

Simplify the left side.

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Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{6} (x \cdot 9) = \log_{6} (54)$

Step 1.2

Move $9$ to the left of $x$ .

$\log_{6} (9 x) = \log_{6} (54)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$9 x = 54$

Step 3

Divide each term in $9 x = 54$ by $9$ and simplify.

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Step 3.1

Divide each term in $9 x = 54$ by $9$ .

$\frac{9 x}{9} = \frac{54}{9}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{54}{9}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{54}{9}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $54$ by $9$ .

$x = 6$