Question

Which expression is equivalent to

Answer 1

The equivalent expression is $log(\frac{1}{2} ) -log_{12}8+log_{12}w$

Logarithms and indices

To get the equivalent expressions for the given logarithmic function, we will use the following laws of logarithm:

Laws of logarithm

• $logab=loga+logb\\ log(\frac{a}{b} )=loga -logb$

Given the logarithmic function:

$log_{12}(\frac{1/2}{8w})$

This can be further expressed as:

$log_{12}(\frac{1/2}{8w} )$$log_{12}(\frac{1/2}{8w} )=log\frac{1}{2}-log8w$

Using the product law of logarithm

$log_{12}(\frac{1/2}{8w}) =log(\frac{1}{2} ) -log_{12}8+log_{12}w$

Hence the equivalent expression is $log(\frac{1}{2} ) -log_{12}8+log_{12}w$

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