Question

log по основанию 6 (х+11)=log по основанию 7 (х+11)

Answer 1

$\displaystyle \log_6(x+11)=\log_7(x+11);$

$\displaystyle \frac{\log(x+11)}{\log(6)}=\frac{\log(x+11)}{\log(7)};$

$\displaystyle \log(x+11)\log(7)=\log(x+11)\log(6);$

$\displaystyle \log(x+11)\log(7)-\log(x+11)\log(6)=0;$

$\displaystyle \log(x+11)\left(\log(7)-\log(6)\right)=0;$

$\displaystyle \log(x+11)=0;$

$\displaystyle x+11=1;$

$\displaystyle \therefore{x=\boxed{-10}\phantom{.}}.$

Answer 2

$log_{6}(x+11)=log_7(x+11) \\ \frac{Log_2(x+11)}{log_26}= \frac{log_2(x+11)}{log_27} \\ log_27log_2(x+11)=log_26log_2(x+11) \\ log_2(x+11)(log_27-log_26)=0 \\ log_2(x+11)=0 \\ x+11=2^0 \\ x+11=1 \\ x=1-11=-10 \\ x+11\ \textgreater \ 0 \iff x\ \textgreater \ -11 \\ x=-10 \ \textgreater \ -11 \\ x=-10$