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

Answer:

A

Step-by-step explanation:

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Answer 2

The system of equations that can represent the equation is,$\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}$.Option A is correct.

What is the definition of a logarithm?

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

The property of the logarithm is found as;

$\rm log_b(a) = \frac{log_x(a)}{log_x(b)}$

Given equation;

$\rm log_4(x+3) = log_2(2+x)$

LHS;

$\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_4(x+3) \\\\ y_1 = \rm y_1 = \frac{log(x+3)}{log 4}$

RHS;

$\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_2(2+x) \\\\ y_2 = \frac{log(2+x)}{log 2}$

The system of equations that can represent the equation is,$\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}$.Option A is correct.

Hence, option A is correct.

To learn more about the logarithm refer ;

https://brainly.com/question/7302008

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