Algebra Examples

$\log (5) + \log (y) = \log (40)$

Step 1

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

$\log (5 y) = \log (40)$

Step 2

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

$5 y = 40$

Step 3

Divide each term in $5 y = 40$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 y = 40$ by $5$ .

$\frac{5 y}{5} = \frac{40}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{40}{5}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{40}{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $40$ by $5$ .

$y = 8$