Question

Calcule, sabendo que log2 = 0,301 e log3 = 0,47
$log_{10}(\frac{25}{8} )$

Answer 1

*Todos os logs na base 10*

log (25/8) = log 25 - log 8

// = [ log (5^2) ] - [ log (2^3) ]

// = [2.log 5] - [3.log 2]

// = [2.log(10/2)] - [3.0,301]

// = [2.(log 10- log 2)] - [0,903]

// = [2.( 1 - 0,301)] - [0,903]

// = [2.0,699] - [0,903]

// = [1,398] - [0,903]

log (25/8) = [1,398] - [0,903] = $0,495$