Logarithm inside another logarithm

Algebra Level 1

$\large \log_{10} \left( \log_{10} 10^{10,000} \right) = \ ?$

3 solutions

Rohit Udaiwal
Sep 28, 2015

$log_{10} \left( \log_{10} 10^{10,000} \right) \\ =log_{10} \left( 10,000×log_{10} 10\right) \\ =log_{10} 10,000 \\ =4$

Nice solution!! :D

Pablo Ruiz - 5 years, 8 months ago

Thank you :P

Rohit Udaiwal - 5 years, 8 months ago

Awesome solution

Adarsh singh - 5 years, 8 months ago

Thank you sir :D!

Rohit Udaiwal - 5 years, 8 months ago

your most welcome sir (Y)

Adarsh singh - 5 years, 5 months ago

David Hall
Sep 28, 2015

$log_{10}(log_{10}(10^{10,000})) = log_{10}(10,000) = log_{10}(10^{4}) = 4$

Ramiel To-ong
Oct 5, 2015

Same analysis