Question

QUAL O VALOR NUMÉRICO DESSA EXPRESSÃO?


log4 (2/log16(4)) +
log4 (√2) + log100 (√0,001) log 1/9 (3√3) 

Answer 1

log4 (2/log16(4)) + log4 (√2) + log100 (√0,001) log 1/9 (3√3) = 
log4(2) - log16 (4) + log4 (√2) + log100( √10^-3) + log1/9 (3√3) = 
log2²(2) - log4² (4) + log2² (√2) + log10² (√10^-3) + log 3^-2 (3√3)= 
1/2 - 1/2 + 1/2log2(2^1/2) + 1/2log10 (10^-3/2) -1/2 log3 (3√3)= 
1/4 - 3/4 - 1/2log3 (3) -1/2log3(√3) = 
1/4 - 3/4 - 1/2 - 1/4 = 
-5/4  
entao o valor numerico dela e 3/2 ou seja tres sobre dois