Precalculus Examples

$2 \log (5) x + \log (5) x^{2} - 10 \log (5) \cdot 5 - \log (5) x^{7}$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\log (5^{2}) x + \log (5) x^{2} - 10 \log (5) \cdot 5 - \log (5) x^{7}$

Step 1.2

Raise $5$ to the power of $2$ .

$\log (25) x + \log (5) x^{2} - 10 \log (5) \cdot 5 - \log (5) x^{7}$

Step 1.3

Simplify $- 10 \log (5)$ by moving $10$ inside the logarithm.

$\log (25) x + \log (5) x^{2} - \log (5^{10}) \cdot 5 - \log (5) x^{7}$

Step 1.4

Raise $5$ to the power of $10$ .

$\log (25) x + \log (5) x^{2} - \log (9765625) \cdot 5 - \log (5) x^{7}$

Step 1.5

Multiply $5$ by $- 1$ .

$\log (25) x + \log (5) x^{2} - 5 \log (9765625) - \log (5) x^{7}$

Step 2

Reorder factors in $\log (25) x + \log (5) x^{2} - 5 \log (9765625) - \log (5) x^{7}$ .

$x \log (25) + x^{2} \log (5) - 5 \log (9765625) - x^{7} \log (5)$