How do you solve #5*11^(5a+10)=57#?

1 Answer
Oct 16, 2016

Answer:

#a=-1.797#

Explanation:

#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