Respuesta :
Properties of Logs
logb(x/y) = logbx - logby.
therefore
log5 (4/7)= log5 (4)- log5 (7)
Solve log 5 (4) and log 5 (7) with the base change of the logarithm
log 5 4 = log 4 / log 5
Use the calculator:
log 5 4 =0.8613531161
log 5 7 = log 7 / log 5
log 5 7 =1.2090619551
log5 (4/7)= log5 (4)- log5 (7)=-0.347708839
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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https://brainly.com/question/20785664
