The approximate value of the expression [tex]log_{5}[/tex] ( [tex]\frac{4}{7}[/tex] ) is -0.3477.
A Logarithm is just another way to express an exponent. Logarithmic properties are used to compress or expend the existing log expression.
Here we use log property for the expansion i.e.,
[tex]log_{b}[/tex] [tex]\frac{x}{y}[/tex] = [tex]log_{b}[/tex] x + [tex]log_{b}[/tex] y
(Note that [tex]log_{b}[/tex]x = [tex]\frac{ log x} {log \\b}[/tex] )
Given,
[tex]log_{5}[/tex] ( [tex]\frac{4}{7}[/tex] )
can be written as:
[tex]log_{5}[/tex] ( [tex]\frac{4}{7}[/tex] ) = [tex]log_{5}[/tex] (4) - [tex]log_{5}[/tex] (7) = [tex]\frac{log 4 - log 7}{log 5}[/tex] = [tex]\frac{0.6020 - 0.8450}{0.69897}[/tex] = - 0.3477
Hence the expression value is -0.3477.
To learn more about log properties, refer to the link:
https://brainly.com/question/15625150
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