Algebra Examples

$5 \log (x) + 3 \log (x^{2})$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log (x)$ by moving $5$ inside the logarithm.

$\log (x^{5}) + 3 \log (x^{2})$

Step 1.2

Simplify $3 \log (x^{2})$ by moving $3$ inside the logarithm.

$\log (x^{5}) + \log ({(x^{2})}^{3})$

Step 1.3

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x^{5}) + \log (x^{2 \cdot 3})$

Step 1.3.2

Multiply $2$ by $3$ .

$\log (x^{5}) + \log (x^{6})$

Step 2

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

$\log (x^{5} x^{6})$

Step 3

Multiply $x^{5}$ by $x^{6}$ by adding the exponents.

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Step 3.1

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

$\log (x^{5 + 6})$

Step 3.2

Add $5$ and $6$ .

$\log (x^{11})$