Question

How do you solve `log(x^3)=(logx)^3`?

Answer 1

x=1, `10^sqrt3, 10^-sqrt3`

Explanation:

`log(x^3)= 3log x`

`3log x= (logx)^3`
`(log x)^3 -3logx =0`

`logx ( (log x)^2-3)`=0

logx=0, `(logx)^2 -3=0`

log x=0 means x=1 and `(logx )^2 -3=0` would mean `log x=+-sqrt3`, or `x=10^sqrt3, 10^-sqrt3`