Question

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

Answer 1

`(x + 3) = 4^(a)` and
`(2 + x) = 2^(a)`

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)