Expand the Logarithmic Expression log base 13 of 6a^3bc^4

$\log_{13} (6 a^{3} b c^{4})$

Step 1

Rewrite $\log_{13} (6 a^{3} b c^{4})$ as $\log_{13} (6 a^{3} b) + \log_{13} (c^{4})$ .

$\log_{13} (6 a^{3} b) + \log_{13} (c^{4})$

Step 2

Rewrite $\log_{13} (6 a^{3} b)$ as $\log_{13} (6 a^{3}) + \log_{13} (b)$ .

$\log_{13} (6 a^{3}) + \log_{13} (b) + \log_{13} (c^{4})$

Step 3

Rewrite $\log_{13} (6 a^{3})$ as $\log_{13} (6) + \log_{13} (a^{3})$ .

$\log_{13} (6) + \log_{13} (a^{3}) + \log_{13} (b) + \log_{13} (c^{4})$

Step 4

Expand $\log_{13} (a^{3})$ by moving $3$ outside the logarithm.

$\log_{13} (6) + 3 \log_{13} (a) + \log_{13} (b) + \log_{13} (c^{4})$

Step 5

Expand $\log_{13} (c^{4})$ by moving $4$ outside the logarithm.

$\log_{13} (6) + 3 \log_{13} (a) + \log_{13} (b) + 4 \log_{13} (c)$

Step 6

Simplify each term.

Rewrite $\log_{13} (6)$ as $\log_{13} (2 (3))$ .

$\log_{13} (2 (3)) + 3 \log_{13} (a) + \log_{13} (b) + 4 \log_{13} (c)$

Rewrite $\log_{13} (2 (3))$ as $\log_{13} (2) + \log_{13} (3)$ .

$\log_{13} (2) + \log_{13} (3) + 3 \log_{13} (a) + \log_{13} (b) + 4 \log_{13} (c)$