How do you solve the equation #1/3logx=log8#?

1 Answer
Dec 3, 2016

Answer:

#x=512#

Explanation:

Using the #color(blue)"laws of logarithms"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx^nhArrnlogx)color(white)(2/2)|)))#

#rArr1/3logx=logx^(1/3)#

#rArrlogx^(1/3)=log8#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx=logyrArrx=y)color(white)(2/2)|)))#

#rArrx^(1/3)=8#

#color(blue)"cubing both sides"#

#rArrx=8^3=512#