Question

Se log2= M + N e Log3 = 2M - N, determine:
Log20 + 2.log50 - log 30

Answer 1

log 20 + 2.log 50 - log 30

log 4.5 + 2.log 5.10 - log 3.10

log 4 + log 5 + 2.(log 5 + log 10) - (log 3 + log 10)

log 2² + log 10/2 + 2.(log 10/2 + log 10) - log 3 - log 10

2.log 2 + log 10 - log 2 + 2.(log 10 - log 2 + log 10) - log 3 - log 10

2.(M + N) + 1 - (M + N) + 2.(1 - (M + N) + 1) - (2M - N) - 1

2M + 2N + 1 - M - N + 2 - 2M - 2N + 2 - 2M + N - 1

2M - 2M - 2M + 2N - 2N - N + N - M + 1 - 1 + 2 + 2

-2M - M + 2 + 2

-3M + 4

Resposta: -3M + 4

Espero ter ajudado.