- #1

- 133

- 5

## Homework Statement

Prove that ##{1/3} < log_{34} 5 < {1/ 2}##

## Homework Equations

##log_b a = {1/ log_a b}##

##logmn = logm + logn##

## The Attempt at a Solution

##log_{34} 5 = {1/ log_5 34}##

##= 1/(log_5 17 + log_5 2)##

##=1/(1 + log_5 3 + log_5 2 + something)##

##=1/(1 + log_5 6 + something)##

##=1/(2+something~else)##

something else ##<1##

Hence it is greater than 1/3 and smaller than 1/2.

But I think mathematically speaking, that ##something## isn't supposed to be there.