Question

se log 2= 0,3 , log 3= 0,5
log 5= 0,7 e log 7= 0,85 , responda:

(exercicios na foto)​

Answer 1

Resposta:

Vide abaixo

Explicação passo-a-passo:

a)

log14 49 =

log14 7^2 =

2. log14 7 =

2. (log 7 / log 14) =

2. (log 7 / log 7. 2) =

2. [ log 7 / (log 7 + log 2) ] =

2. [0,85 / (0,85 + 0,3)] =

2. 0,85/ 1,15 =

~ 1,478

b)

log12 64 =

log12 8^2 =

2. log12 8 =

2. log12 2^3 =

2.3. log12 2 =

6. log12 2 =

6. (log 2 / log 12) =

6. (log 2 / log 4.3) =

6. [ log 2 / (log 4 + log 3) ] =

6. [ log 2 / (log 2^2 + log 3) ] =

6. [ log 2 / (2.log 2 + log 3) ] =

6. [ 0,3 / (2. 0,3 + 0,5) ] =

6. 0,3 / 1,1 =

~ 1,636

c)

log21 40 =

log21 8.5 =

log21 8 + log21 5 =

log21 2^3 + log21 5 =

3. log21 2 + log21 5 =

3. (log 2 / log 21) + (log 5 / log 21) =

3. (log 2 / log 7. 3) + (log 5 / log 7. 3) =

3. (log 2 / (log 7 + log 3)) + (log 5 / (log 7 + log 3)) =

3. (0,3 / (0,85 + 0,5)) + (0,7 / (0,85 + 0,5)) =

0,9/ 1,35 + 0,7/ 1,35 =

1,6/ 1,35 =

~ 1,185

d)

log0,05 0,03 =

log0,05 3/100 =

log0,05 3 - log 0,05 100 =

log 3 / log 0,05 - log 100 / log 0,05 =

log 3 / log 5/100 - 2 / log 5/100 =

log 3 / (log 5 - log 100) - 2 / (log 5 - log 100) =

0,5 / (0,7 - 2) - 2 / (0,7 - 2) =

(0,5 - 2) / (0,7 - 2) =

-1,5 / -1,3 =

~ 1,154

Blz?

Abs :)