Question

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

Answer 1

Product Law

Answer 2

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

Answer 3

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)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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.