Question

dados log 2=a e log 3=b, determineç log 6, log 24, log 300, log 1,5 , log 16

Answer 1

Resposta:

a + b

3a + b

2 + b

b - a

4a

Explicação passo-a-passo:

24 = 8.3 = 3 . 2³

6 = 2 . 3

300=100.3 = 10² . 3

1,5 = 15/10 = 3/2

16 = 2⁴

loga . b = loga + lgb

loga/b = loga - logb

logaⁿ = n.loga

log10 = 1

log 6 =log2.3 = log2 + log3 =  a + b

log 24 = log3.2³ = log3 + log2³ = log3 + 3log2 = b + 3a = 3a + b

log 300 = log 10² . 3 = log10² + log3 = 2log10 + log3 = 2.1 + b = 2 + b

log 1,5 = log3/2 = log3 - log2 = b - a

log 16 = log2⁴ = 4log2 = 4a