Calculus Examples

$\log (3 x) = \log (2) + \log (x + 5)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $\log (2) + \log (x + 5)$ .

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Step 1.1.1

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

$\log (3 x) = \log (2 (x + 5))$

Step 1.1.2

Apply the distributive property.

$\log (3 x) = \log (2 x + 2 \cdot 5)$

Step 1.1.3

Multiply $2$ by $5$ .

$\log (3 x) = \log (2 x + 10)$

Step 2

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

$3 x = 2 x + 10$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$3 x - 2 x = 10$

Step 3.2

Subtract $2 x$ from $3 x$ .

$x = 10$