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Which expression is equivalent to log Subscript c Baseline StartFraction x squared minus 1 Over 5 x EndFraction?
log Subscript c Baseline x squared minus log Subscript c Baseline 5 x minus 1
2 log Subscript c Baseline x minus (log Subscript c Baseline 5 + log Subscript c Baseline x) minus 1
log Subscript c Baseline (x squared minus 1) minus (log Subscript c Baseline 5 + log Subscript c Baseline x)
2 log Subscript c Baseline x minus log Subscript c Baseline 1 minus log Subscript c Baseline 5 + log Subscript c Baseline x

Answer :

MRROYALGO

The equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

How to determine the equivalent expression?

The logarithmic expression is given as:

[tex]\log_c(\frac{x^2 - 1}{5x})[/tex]

The law of logarithm states that:

log(a) - log(b) = log(a/b)

This means that the expression can be split as:

[tex]\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)[/tex]

Hence, the equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

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