Algebra Examples

$\log (9 t^{3} - 5 t) + \log (t^{- 1})$

Step 1

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

$\log ((9 t^{3} - 5 t) t^{- 1})$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\log ((9 t^{3} - 5 t) \frac{1}{t})$

Step 3

Multiply $9 t^{3} - 5 t$ by $\frac{1}{t}$ .

$\log (\frac{9 t^{3} - 5 t}{t})$

Step 4

Factor $t$ out of $9 t^{3} - 5 t$ .

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Step 4.1

Factor $t$ out of $9 t^{3}$ .

$\log (\frac{t (9 t^{2}) - 5 t}{t})$

Step 4.2

Factor $t$ out of $- 5 t$ .

$\log (\frac{t (9 t^{2}) + t \cdot - 5}{t})$

Step 4.3

Factor $t$ out of $t (9 t^{2}) + t \cdot - 5$ .

$\log (\frac{t (9 t^{2} - 5)}{t})$

Step 5

Cancel the common factor of $t$ .

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Step 5.1

Cancel the common factor.

$\log (\frac{t (9 t^{2} - 5)}{t})$

Step 5.2

Divide $9 t^{2} - 5$ by $1$ .

$\log (9 t^{2} - 5)$