The log expression equivalent to [tex]log_c(\frac{x^2-1}{5x} )[/tex] is [tex]log_c(x^2 -1)-(log_c5+log_cx)[/tex]
Law of logarithm
Given the logarithmic function
[tex]log_c(\frac{x^2-1}{5x} )[/tex]
We need to look for an equivalent log expression. According to the option C expressed as:
[tex]log_c(x^2 -1)-(log_c5+log_cx)[/tex]
Since addition is equivalent to product, hence;
[tex]log_c(x^2 -1)-(log_c5x)[/tex]
Takin the quotient of the result will give;
[tex]log_c(x^2 -1)-(log_c5x)=log_c(\frac{x^2-1}{5x})[/tex]
Hence the log expression equivalent to [tex]log_c(\frac{x^2-1}{5x} )[/tex] is [tex]log_c(x^2 -1)-(log_c5+log_cx)[/tex]
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