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Question

Write the expression as a single logarithm.

4log₆x-1/5 log₆z + 2log₆y

Answer 1

Use the Product, Quotient, and Power Rules of Logarithms:

loga (x) + loga (y) <==> loga (xy)

adding like bases? multiply the arguments (Product Rule)

loga (x) - loga (y) <==> loga (x/y)

subtracting like bases? divide the arguments (Quotient Rule)

loga (x)^(y) <==> y loga (x)

raising an argument to a power? multiply the answer by the power (Power Rule)

Rewrite the terms of the log expression 4log₆ x - 1/5log₆ z + 2log₆ y using the Power Rule:

4 log₆ x = log6 x⁴

1/5 log₆ z = log6 z^(1/5)

2 log₆ y = log6 y²

Combine the terms using the Product and Quotient Rules:

log₆ x⁴ * log₆ y² / log₆ z^(1/5)

Factor log₆ from each term and you get Ray's correct answer!

Answer 2

log6 [x^4 * y^2 / z^(1/5) ]