Question

Log2(log5(625)) find the value

Answer 1

Answer:

2

Explanation:

log2(log5^5^4

log2^4

log2^2^2=2

Answer 2

Need To Find Out:-

• Value of $\sf \: ( log_{2}( log_{5}(625) )$

Solution :-

We are given :-

$\sf :\implies \ \: ( log_{2}( log_{5}(625) )$

$\sf \underline\green {Let \: consider:- }$

$\sf\purple{ :\implies \: log_{5}(625)}$

$\sf \: = \: \: log_{5}(5 \times 5 \times 5 \times 5)$

$\sf \: = \: \: log_{5}( {5}^{4} )$

$\sf \: = \: \: 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\green{\{ \because \: log_{ {a}^{p} }( {a}^{q}) = \dfrac{q}{p} \}}}$

$\boxed{\sf\purple{:\implies \: log_{5}(625) = 4}}$

$\sf \underline\green {Now:-}$

$\sf\purple{:\implies \ \: log_{2}( log_{5}(625) )}$

$\sf \: = \: \: \: log_{2}( 4 )$

$\sf \: = \: \: \: log_{2}( 2 \times 2 )$

$\sf \: = \: \: \: log_{2}( {2}^{2})$

$\sf\: = \: \: 2\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\green{\{ \because \: log_{ {a}^{p} }( {a}^{q}) = \dfrac{q}{p} \}}}$

$\sf\therefore\pink{ \: \: ( log_{2}( log_{5}(625) ) = 2}$

Know More :-

• $\sf \:logx + logy = logxy$
• $\sf \:logx - logy = log \dfrac{x}{y}$
• $\sf \:log \: {x}^{y} = y \: logx$
• $\sf\: log_{x}(x) = 1$
• $\sf \: log_{x}(y) = \dfrac{logy}{logx}$
• $\sf \:log1 = 0$
• $\sf\: {e}^{ log(x)} = x$
• $\sf\: {e}^{ ylog(x)} = {x}^{y}$
• $\sf\: {x}^{ log_{x}(y) } = y$
• $\sf \: {x}^{z log_{x}(y) } = {y}^{z}$