The equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
Logarithms and indices
To get the equivalent expressions for the given logarithmic function, we will use the following laws of logarithm:
Laws of logarithm
- [tex]logab=loga+logb\\
log(\frac{a}{b} )=loga -logb[/tex]
Given the logarithmic function:
[tex]log_{12}(\frac{1/2}{8w}) [/tex]
This can be further expressed as:
[tex]log_{12}(\frac{1/2}{8w} )[/tex][tex]log_{12}(\frac{1/2}{8w} )=log\frac{1}{2}-log8w [/tex]
Using the product law of logarithm
[tex]log_{12}(\frac{1/2}{8w}) =log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
Hence the equivalent expression is [tex]log(\frac{1}{2} ) -log_{12}8+log_{12}w[/tex]
Learn more on logarithm here: https://brainly.com/question/247340
