[tex]\displaystyle\\
\text{Folosim formulele: }\\\\
\frac{1}{\log_b a} =\log_a b ~~~a,b \ \textgreater \ 0; ~~a,b \neq 1\\\\
\log_a b \cdot \log_b c = \log_a c ~~~a,b,c \ \textgreater \ 0; ~~a,b \neq 1\\\\\\
\text{Rezolvare: }\\
\text{Scriem: } \lg x = log_{_{10}}x~~\text{si}~~\ln x = log_e\,x \\\\
\frac{\ln15}{\lg15}=\frac{log_e15}{log_{_{10}}15}=log_e15 \cdot\frac{1}{log_{_{10}}15}=log_e15 \cdot log_{_{15}}10}=log_e 10 =\boxed{\ln10}
[/tex]
