Algebra Examples

$3 \log (x) + \log (2 x + 1)$

Step 1

Simplify $3 \log (x)$ by moving $3$ inside the logarithm.

$\log (x^{3}) + \log (2 x + 1)$

Step 2

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

$\log (x^{3} (2 x + 1))$

Step 3

Apply the distributive property.

$\log (x^{3} (2 x) + x^{3} \cdot 1)$

Step 4

Simplify the expression.

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Step 4.1

Rewrite using the commutative property of multiplication.

$\log (2 x^{3} x + x^{3} \cdot 1)$

Step 4.2

Multiply $x^{3}$ by $1$ .

$\log (2 x^{3} x + x^{3})$

Step 5

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

$\log (2 (x \cdot x^{3}) + x^{3})$

Step 5.2

Multiply $x$ by $x^{3}$ .

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Step 5.2.1

Raise $x$ to the power of $1$ .

$\log (2 (x^{1} x^{3}) + x^{3})$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log (2 x^{1 + 3} + x^{3})$

Step 5.3

Add $1$ and $3$ .

$\log (2 x^{4} + x^{3})$