Question

Consider the equation below. Log Subscript 4 Baseline (x 3) = log Subscript 2 Baseline (2 x) Which system of equations can represent the equation? y 1 = StartFraction log (x 3) Over log 4 EndFraction, y 2 = StartFraction log (2 x) Over log 2 EndFraction y 1 = StartFraction log x 3 Over log 4 EndFraction, y 2 = StartFraction log 2 x Over log 2 EndFraction y 1 = StartFraction log 4 Over log 2 EndFraction, y 2 = StartFraction log (x 3) Over log (2 x) EndFraction y 1 = StartFraction log x 3 Over 4 EndFraction, y 2 = StartFraction log 2 x Over 2 EndFraction.

Answer 1

Equivalent equations are equations of equal values

The system of equations from the given equation are:

$y= \log_2(2x)$ and $y=3\log_4(x)$

The logarithmic equation is given as:

$\log_4(x^3) = \log_2(2x)$

Split the above equation as follows:

$y = \log_4(x^3)$

$y= \log_2(2x)$

Rewrite $y = \log_4(x^3)$ as:

$y=3\log_4(x)$

Hence, the system of equations from the given equation are:

$y= \log_2(2x)$ and $y=3\log_4(x)$

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