Hi,

I don't see where I"m going wrong in these. Forgive me for the simple errors

Express in terms of log a, log b, and log c.

$\displaystyle \log \bigg(\sqrt[a]{\big(\frac{b}{c^3}\big)}\bigg)$

$\displaystyle \log \bigg(\bigg(\frac{b}{c^3}\bigg)^\frac{1}{a}\bigg)$

$\displaystyle \frac{1}{a} \log b - \frac{1}{a} 3 \log c$

Answer given: $\displaystyle \log a + \frac{1}{2} \log b - \frac{3}{2} \log c$

Express as a single logarithm

$\displaystyle 3 \log_a 3 - \log_a 15 + 2 \log_a 5$

$\displaystyle = \log_a 9 - \log_a 15 + \log_a 25$

$\displaystyle = \log_a \big(\frac{9}{15}\big) + \log_a 25$

$\displaystyle = \log_a \big(\frac{3}{5} \times 25\big)$

$\displaystyle = \log_a 15$

Answer given: $\displaystyle \log_a 45$