Log (2) 3 and Ln3 are used to judge the size. For example, how can we judge the size if it is different from the true number base?

Log (2) 3 and Ln3 are used to judge the size. For example, how can we judge the size if it is different from the true number base?

Generally, the formula of changing bottom is used
If the base number is different, the true number is the same,
Log (2) 3 and Ln3,
ln3=lg3/lge,
log（2)3=lg3/lg2,
lge>lg2>0,
∴log(2)3>ln3

Log base is 7, true number is 5 and log base is 6, true number is 7

The log base number is 7 and the true number is 51
Log base is 7, true number is 5 < log base is 6, true number is 7

Inequality log3 (5-x)

5-x>0
3x+1>0
5-x1
therefore
one