Question

Which system of equations could be graphed to solve the equation below? log Subscript 0. 5 Baseline x = log Subscript 3 Baseline 2 x.

Answer 1

You can use the fact that two expressions in equality can be considered to be equal to a third variable(not used in given context).

The system of equations that could be graphed to solve the equation given is

• $y = \log_{0.5}(x)$
• $y = \log_3(2+x)$

How can we form a system of equations from an equation?

Suppose the equation be $a = b$

Let there is a symbol $c$ such that we have $a = b = c$

It is because a and b are same measure (that is exactly what a = b means)

and we gave another name c to that measure.

Thus, we have

$a = c\\b = c$

in addition to  $a = b$

Using the above method to find the system of equations needed

Since the given equation is $log_{0.5}(x) = log_2(2+x)$

The 2d graphs are usually expressed as $y = f(x)$ on X-Y plane.

Taking the equation's expressions equal to y, we get

$log_{0.5}(x) = log_2(2+x) = y$

or, we get system of equations as

$y = log_{0.5}(x)\\\\y = log_3{(2 + x)}$

Their graph is plotted below. The intersection point of both curves is the solution to the given equation as it satisfies both the equations of the system of equations formed from the given equation.

Thus,

The system of equations that could be graphed to solve the equation given is

• $y = \log_{0.5}(x)$
• $y = \log_3(2+x)$

Learn more about solutions to system of equations here:

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