Approximate: log5 4/7

The basic properties of a logarithmic function is the properties which can be used to simplify any logarithmic function. In solving the given function, the logarithmic properties used are:

[tex]log_A\dfrac{B}{C}=log_AB-log_AC[/tex]

[tex]log_AB=\dfrac{log_gB}{log_gA}[/tex]

Hence, the approximate value of the logarithmic function [tex]\bold{A=log_5\dfrac{4}{7}}[/tex] is -0.348.

Given information:

The logarithmic expression is given in the question in order to get the approximate value of the expression,

[tex]\bold{A=log_5\dfrac{4}{7}}[/tex]

As, we know that one of the property of a logarithmic function is,

[tex]log_A\dfrac{B}{C}=log_AB-log_AC[/tex]

Now, use the above property of log to simplify the given expression,

[tex]A=log_5\dfrac{4}{7}\\\\A=log_5(4)-log_5(7)[/tex]

According to the property of a logarithmic function , we can write,

[tex]log_AB=\dfrac{log_gB}{log_gA}[/tex]

Now, applying this property of logarithmic function in the given expression, we get,

[tex]A=\dfrac{log4}{log5}-\dfrac{log7}{log5} \\\\A=0.861-1.209\\A=-0.348[/tex]

Hence, the approximate value of the logarithmic function [tex]\bold{A=log_5\dfrac{4}{7}}[/tex] is -0.348.

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