# Math Help - Logarithms

1. ## Logarithms

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.

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

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

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

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

Express as a single logarithm

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

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

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

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

$= \log_a 15$

Answer given: $\log_a 45$

Note that: $3\log_a(3)=\log_a(27).$

3. Thank you

$= \log_a 27 - \log_a 15 + 2 \log_a 25$

$= \log_a \big(\frac{27}{15}\big) + \log_a 25$

$= \log_a \big(\frac{9}{5} \times 25\big)$

$= \log_a 45$

4. .

5. Originally Posted by Hellbent
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.

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

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

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

Answer given: $\log a + \frac{1}{2} \log b - \frac{3}{2} \log c$
IF the problem were $log\left(a\sqrt{\frac{b}{c^3}}\right)$
rather than $log\sqrt[a]{\frac{b}{c^3}}$ then the given answer would be correct.
Express as a single logarithm

[tex]3 \log_a 3 - \log_a 15 + \log_a 5[/MATH $= \log_a 9 - \log_a 15 + \log_a 25$]
$3^3= 27$, not 9. How did that last "5" become "25"?

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

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

$= \log_a 15$

Answer given: $\log_a 45$

6. Originally Posted by HallsofIvy
IF the problem were $log\left(a\sqrt{\frac{b}{c^3}}\right)$
rather than $log\sqrt[a]{\frac{b}{c^3}}$ then the given answer would be correct.

$3^3= 27$, not 9. How did that last "5" become "25"?
I fixed it. Thanks.