EquationSolve the equation  log logx=1

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation to be solved is: log (log x) = 1

log represents logarithm to the base 10. And log 10 = 1

log (log x) = 1

=> log (log x) = log 10

=> log x = 10

=> x = 10^10

The solution of the equation is x = 10^10

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll impose constraint of existence of logarithms:

x>0

We know that the inverse function of exponential function is ligarithmic function.

We consider the exponential function:

f(x) = a^x, a>0

a^x = b

To compute x, we'll take decimal logarithms both sides:

log a^x = log b

The power rule of logarithms claims that:

log a^x = x* log a

x* log a = log b

x = log b/log a

If we have the function f(x) = log x

log a x = b

We'll take antilogarithms to calculate x:

x = a^b

So, we'll take antilogarithm to solve the given equation.

log x = 10^1

Log x = 10

We'll take again the antilogarithm, to compute x:

x = 10^10

Remark: Since the base is not indicated, we suppose that the base of both logarithms is 10.

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