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Bad White [126]
3 years ago
5

Condense the following log into a single log:

Mathematics
1 answer:
Tasya [4]3 years ago
6 0

Answer:

log_{3}(x . y^\frac{1}{3} / z^5 )

Step-by-step explanation:

Given in the question an expression

log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z

To Condense this log into a single log we will use logarithm rules

<h3>1)Power rule</h3>

logb(x^y) = y ∙ logb(x)

\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}

5log_{3} z = log_{3} z^5

<h3>2)Product rule</h3>

logb(x ∙ y) = logb(x) + logb(y)

log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )

<h3>3)qoutient rule </h3>

logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5

= log_{3}(x . y^\frac{1}{3} / z^5 )

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