Question

Condense the following log into a single log:

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

Answer 1

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

1)Power rule

logb(x^y) = y ∙ logb(x)

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

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

2)Product rule

logb(x ∙ y) = logb(x) + logb(y)

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

3)qoutient rule

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

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