Pre-Algebra Examples

$2 \log (x) - 0$ , $5 \log (x^{2})$

Step 1

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

$\log (x^{2}) - 0 + 5 \log (x^{2})$

Step 2

Multiply $- 1$ by $0$ .

$\log (x^{2}) + 0 + 5 \log (x^{2})$

Step 3

Simplify $5 \log (x^{2})$ by moving $5$ inside the logarithm.

$\log (x^{2}) + 0 + \log ({(x^{2})}^{5})$

Step 4

Multiply the exponents in ${(x^{2})}^{5}$ .

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Step 4.1

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

$\log (x^{2}) + 0 + \log (x^{2 \cdot 5})$

Step 4.2

Multiply $2$ by $5$ .

$\log (x^{2}) + 0 + \log (x^{10})$

Step 5

Add $\log (x^{2})$ and $0$ .

$\log (x^{2}) + \log (x^{10})$

Step 6

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

$\log (x^{2} x^{10})$

Step 7

Since there are no common prime factors, the GCF is $1$ .

$1$