Question

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

Answer 1

`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`