1. Log Help

Hi, need some help on these questions:

16. Express logx in terms of log a, log b, and log c given that $x = a^2 \sqrt{b^3 c}$

20. $log_{a}2 = log_{b}16$, show that $b = a^4$

21. Find values of x for which:
a) $(log_{10}x)(log_{10}x^2) + log_{10}x^3 - 5 = 0$
b) $(log_{10}x)^2 - log_{10}x^2 +1 = 0$
c) $(log_{2}x^2)^2 - log_{2}x^3 - 10 = 0$
d) $(log_{3}x)^2 = log_{3}x^5 - 6$

2. 16. Use the same rule I posted to your earlier thread.

$\log\ a + \log\ b = \log\ ab$

and one more: $\log\ a^b = b\log\ a$

Here, you have:

$\log\ x = \log\ a^2\sqrt{b^3c}$

Can you simplify?

20. Do you know how to change the base?

$\log_y\ x = \dfrac{\log_z\ x}{\log_z\ y}$

Where z can be any base you want, but you can choose one which will suit what you want to do.

21. For those, use $\log\ a^b = b\log\ a$ first, then make a substitution to help you. $\log_k\ x = y$ where k is the base used. When you simplified, you can solve for y, then plug the log back. From there, you should be able to solve for x.

Can you show what you come up with?