Question

Which system of equations can represent the equation log4(x+3)=log2(2+x)

Answer 1

Answer:

$(x + 3) = 4^{a}$ and $(2 + x) = 2^{a}$

Step-by-step explanation:

We are give that $\log_{4} {(x + 3)} = \log_{2} {(2 + x)}$

Now, we have to represent this equation into a system of equations.

Let, $\log_{4} {(x + 3)} = \log_{2} {(2 + x)} = a$

Therefore, we can write $\log_{4} {(x + 3)} = a$

⇒ $(x + 3) = 4^{a}$ ........ (1)

{We know that if $\log_{b} (a) = c$, then converting the logarithm function to exponential function we can write $a = b^{c}$}

Again, we can write $\log_{2} {(2 + x)} = a$

⇒ $(2 + x) = 2^{a}$ ........... (2)  

Hence, equations (1) and (2) are the required system of equations. (Answer)