Question

find the logarithm of 400/to the base 2√5​

Answer 1

Answer:

$log_{2 \sqrt{5} }(400 ) \\ = log_{2 \sqrt{5} }( {20}^{2} ) \\ = 2 log_{2 \sqrt{5} }(20) \\ = 2 log_{ \sqrt{20} }(20) \\ = 2 log_{ {20}^{ \frac{1}{2} } }(20) \\ = 2 / \frac{1}{2} log_{20}(20) \\ = 2 \times 2 \\ = 4$

formula:

log a base a =1

hope this helps you☺️☺️

Answer 2

Answer:

$\bold\red{4}$

Step-by-step explanation:

$log_{2 \sqrt{5} }(400) \\ \\ = log_{ \sqrt{4 \times 5} }(400) \\ \\ = log_{ \sqrt{20} }(400) \\ \\ = log_{ {20}^{ \frac{1}{2} } }(400) \\ \\ = 2 log_{20}(400) \\ \\ = 2 log_{20}( {20}^{2} ) \\ \\ = 2 \times 2 log_{20}(20) \\ \\ = 4 \times 1 \\ \\ 4$

Properties of logarithms involved here are :-

$log_{ {a}^{x} }( {b}^{y} ) = \frac{y}{x} log_{a}(b)$

$log_{a}(a) = 1$