3 years ago

Prove that 1÷loga ab + 1÷logb ab=1

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

6 0

Answer:

See below.

Step-by-step explanation:

1 ÷ loga ab + 1 ÷ logb ab

= 1 / (loga ab) + 1 / (loga ab / loga b) { change of log base)

= 1 / (loga ab) + loga b / (loga ab)

= (1 + loga b) / loga ab

= (1 + loga b) / (loga a + loga b) Now loga a = 1 so we have:

((1 + loga b) / (1 + loga b)

= 1.

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Prove that 1÷loga ab + 1÷logb ab=1​

Prove that 1÷loga ab + 1÷logb ab=1