Question

log(logx)=2
Solve for x

Answer 1

Use definition of log.
Using base 10, log(x) = y means 10^y = x
log(logx) = 2 means 10^2 = log x
Use the definition again:
log x = 10^2 means 10^(10^2) = x
x = 10^(10^2)
If the base is e instead of x, then pelace the 10's in the answer with e's

Answer 2

log(logx)=2

Let both sides of the equation be the exponent of base 10.
10^(log(logx))=10^(2)

When the base of a logarithm in the exponent and the base of the exponent are the same, the result is the argument of the logarithm.
logx=10^(2)

Squaring a number is the same as multiplying the number by itself (10*10).

logx=10*10

Multiply 10 by 10 to get 100.
logx=100

Let both sides of the equation be the exponent of base 10.
10^(logx)=10^(100)

When the base of a logarithm in the exponent and the base of the exponent are the same, the result is the argument of the logarithm.
x=10^(100)

Raising a number to the 100th power is the same as multiplying the number by itself 100 times.
x=1E+100

Answer 3

*replace (not pelace)^

Answer 4

Thank you all for the help. This looks easy now ;-)