Evaluate log of log of 10^10000

$\log (\log (10^{10000}))$

Step 1

Use logarithm rules to move $10000$ out of the exponent.

$\log (10000 \log (10))$

Step 2

Logarithm base $10$ of $10$ is $1$ .

$\log (10000 \cdot 1)$

Step 3

Multiply $10000$ by $1$ .

$\log (10000)$

Step 4

Logarithm base $10$ of $10000$ is $4$ .

Rewrite as an equation.

$\log (10000) = x$

Rewrite $\log (10000) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{x} = 10000$

Create equivalent expressions in the equation that all have equal bases.

$10^{x} = 10^{4}$

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

$x = 4$

The variable $x$ is equal to $4$ .

$4$

Evaluate log of log of 10^10000

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