## anonymous 4 years ago Logarithm Question!!!

1. anonymous

Evaluate in terms of p $\log_{c} b$ if ... $\log_{b}a =p$ and c=a^2

2. hartnn

put a = $$\sqrt c$$ in that and tell me what u get ?

3. anonymous

log _b (root c) = p

4. hartnn

right , now use the property that $$\log x^y=y \log x$$ so what will be $$\log_b c^{1/2} = ?$$

5. anonymous

1/2 (log_b (c))

6. hartnn

right, that is p, so what is (log_b (c)) = ?

7. dumbcow

what a fun problem...i won't spoil the solution and let hartnn explain the steps

8. anonymous

um....2p

9. hartnn

thats correct. then use the property that $$\huge \log_xy=\frac{\log y}{\log x} = \frac{1}{\log_yx}$$

10. hartnn

(log_b (c)) = 2p so whats (log_c (b)) = ?

11. anonymous

lol i am not fimiliar with that property.. but it equals 1/(2p)

12. hartnn

yes, 1/(2p) is correct. its one of the very useful properties of log. u want a list of all the log properties ?

13. anonymous

14. hartnn
15. anonymous

thank you!

16. hartnn

welcome ^_^