## anonymous 4 years ago How do you solve: 2 log base 4 of 3 + log base 4 of 2 WITHOUT A CALCULATOR?

1. lgbasallote

Product Law

2. anonymous

start with $\log_4(3^2)+\frac{1}{2}$

3. dumbcow

use log property: log x +logy = log xy and log x^n = n*log x --> log base 4 (3^2 *2) = log base 4 (18)

4. anonymous

then $\log_4(9)=\frac{\ln(9)}{\ln(4)}$

5. anonymous

oh without a calculator! you cannot do it, you can just rewrite it

6. anonymous

Well without a calculator log base 4 of 2=1/2. And 2 log base 4 of 3 can be written as 2 log 3/log 4(Both to base 10) Log 4=2log 2 so it becomes log 3/log 2(Which values it think you should remember )=0.4771/0.3010. So it becomes 4771/3010+ 0.5

7. Mertsj

Please check you book and make sure you have posted the problem EXACTLY as it is in your book. A little detail can make a HUGE difference.