Answer:
[tex](x + 3) = 4^{a}[/tex] and [tex](2 + x) = 2^{a}[/tex]
Step-by-step explanation:
We are give that [tex]\log_{4} {(x + 3)} = \log_{2} {(2 + x)}[/tex]
Now, we have to represent this equation into a system of equations.
Let, [tex]\log_{4} {(x + 3)} = \log_{2} {(2 + x)} = a[/tex]
Therefore, we can write [tex]\log_{4} {(x + 3)} = a[/tex]
⇒ [tex](x + 3) = 4^{a}[/tex] ........ (1)
{We know that if [tex]\log_{b} (a) = c[/tex], then converting the logarithm function to exponential function we can write [tex]a = b^{c}[/tex]}
Again, we can write [tex]\log_{2} {(2 + x)} = a[/tex]
⇒ [tex](2 + x) = 2^{a}[/tex] ........... (2)
Hence, equations (1) and (2) are the required system of equations. (Answer)
