Basic Math Examples

$\ln (a) + \ln (b) = \ln (a + b)$

Step 1

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

$\ln (a b) = \ln (a + b)$

Step 2

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

$a b = a + b$

Step 3

Solve for $a$ .

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Step 3.1

Subtract $a$ from both sides of the equation.

$a b - a = b$

Step 3.2

Factor $a$ out of $a b - a$ .

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Step 3.2.1

Factor $a$ out of $a b$ .

$a (b) - a = b$

Step 3.2.2

Factor $a$ out of $- a$ .

$a (b) + a \cdot - 1 = b$

Step 3.2.3

Factor $a$ out of $a (b) + a \cdot - 1$ .

$a (b - 1) = b$

Step 3.3

Divide each term in $a (b - 1) = b$ by $b - 1$ and simplify.

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Step 3.3.1

Divide each term in $a (b - 1) = b$ by $b - 1$ .

$\frac{a (b - 1)}{b - 1} = \frac{b}{b - 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $b - 1$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{a (b - 1)}{b - 1} = \frac{b}{b - 1}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{b}{b - 1}$