Question

Find the approximate value of $\log_{e}$ (101) given $\log_{e}$ 10 = 2.3026

Answer 1

Notice, lnln is a natural logarithm on base ee(an irrational number) while loglog is a common logarithm on base 10 which are correlated as follows
[Math Processing Error]
Hence, lne=logee=1ln⁡e=loge⁡e=1 &
loge=log10e=1loge10=1ln10=12.303=0.434294481log⁡e=log10⁡e=1loge⁡10=1ln⁡10=12.303=0.434294481
⟹lne=logee=loge10⋅log10e=2.303log10e