Use properties of logarithms to show that log(3) + log(4) + log(5) − log(6) = 1

⇒ ( log(3) + log(4) ) + log(5) − log(6)

or

⇒ log(3 × 4) + log(5) - log(6)

or

⇒ log(12) + log(5) - log(6)

or

⇒ log(12 × 5) - log(6)

or

⇒ log(60) - log(6)

or

⇒

or

⇒ log(10)

also,

log(10) = 1

Step-by-step explanation:

Given equation;

log(3) + log(4) + log(5) − log(6) = 1

now, we know the property of log function as:

1) log(A) + log(B) = log(AB)

and,

2) log(A) - log(B) =

therefore, applying the property (1) on the LHS

⇒ ( log(3) + log(4) ) + log(5) − log(6)

or

⇒ log(3 × 4) + log(5) - log(6)

or

⇒ log(12) + log(5) - log(6)

again applying the property (1)

⇒ log(12 × 5) - log(6)

or

⇒ log(60) - log(6)

now applying the property 2, we get

⇒

or

⇒ log(10)

also,

log(10) = 1

Hence,

LHS = 1 = RHS

Hence, proved

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step-by-step explanation:

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