Write as a Single Logarithm 3 log of a+ log of a-2

$3 \log (a) + \log (a - 2)$

Step 1

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

$\log (a^{3}) + \log (a - 2)$

Step 2

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

$\log (a^{3} (a - 2))$

Step 3

Apply the distributive property.

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

Step 4

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

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

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

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

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

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

Add $3$ and $1$ .

$\log (a^{4} + a^{3} \cdot - 2)$

Step 5

Move $- 2$ to the left of $a^{3}$ .

$\log (a^{4} - 2 a^{3})$