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

[latex]displaystyle log_6(x+11)=log_7(x+11);[/latex][latex]displaystyle frac{log(x+11)}{log(6)}=frac{log(x+11)}{log(7)};[/latex][latex]displaystyle log(x+11)log(7)=log(x+11)log(6);[/latex][latex]displaystyle log(x+11)log(7)-log(x+11)log(6)=0;[/latex][latex]displaystyle log(x+11)left(log(7)-log(6)ight)=0;[/latex][latex]displaystyle log(x+11)=0;[/latex][latex]displaystyle x+11=1;[/latex][latex]displaystyle herefore{x=oxed{-10}phantom{.}}.[/latex]

[latex]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 extgreater 0 iff x extgreater -11 \ x=-10 extgreater -11 \ x=-10[/latex]