#5 * 11^(5a+10)=57#

#(5*11^(5a+10))/5=57/5color(white)(aaa)#*Divide both sides by 5*

#11^(5a+10)=57/5#

#log(11^(5a+10))=log (57/5)color(white)(aaa)#*Take the log of both sides*

#(5a+10)log11=log(57/5)color(white)(aa)#*Use the log rule* #logx^a=alogx#

#frac{(5a+10)log11}{log11}=frac{log(57/5)}{log11}color(white)(aa)#*Divide both sides by log11*

#5a+10=frac{log(57/5)}{log11}#

#color(white)(aa)-10color(white)(aaa)-10color(white)(aaa)#*Subtract 10 from both sides*

#5a=frac{log(57/5)}{log11}-10#

#(5a)/5=frac{frac{log(57/5)}{log11}-10}{5}color(white)(aaa)#*Divide both sides by 5*

#a=-1.797color(white)(aaa)#*Use a calculator*