log(base 2) (x=2)= log(base 2)x squared
opps its log(base2) (x+2)= log(base2) x squared
"antilog" both sides to get
x+2 = x^2
x^2 - x - 2 = 0
can you take it from here?
whats the up arrow thingy mean?
nevermind i got it yea thank you
i can do it
To understand why log(base 2)(x+2) is equal to log(base 2)(x^2), we can examine the properties of logarithms.
First, we need to understand the property of logarithms called the power rule. According to the power rule, for any base (let's say b) and any positive real numbers x and y, log(base b)(x^y) is equal to y times log(base b)(x). This allows us to simplify logarithmic expressions when there are exponents involved.
Now let's apply this rule to the given expression: log(base 2)(x+2).
We can rewrite x+2 as (x^1) + (2^1) because any value raised to the power of 1 is the same value.
Using the power rule, we can now write log(base 2)(x+2) as 1 * log(base 2)(x) + 1 * log(base 2)(2).
The second term, log(base 2)(2), simplifies to 1, because log(base b)(b) is always equal to 1 for any base b. Therefore, 1 * log(base 2)(2) is simply 1.
Simplifying further, we have log(base 2)(x+2) = log(base 2)(x) + 1.
Now, let's consider the expression log(base 2)(x^2).
Using the power rule, we can rewrite x^2 as (x^1) * (2^1), because x^2 is equal to x^(2*1).
Applying the rule, log(base 2)(x^2) becomes 1 * log(base 2)(x) + 1 * log(base 2)(2).
As mentioned earlier, log(base 2)(2) simplifies to 1.
Therefore, we have log(base 2)(x^2) = log(base 2)(x) + 1.
We can observe that both log(base 2)(x+2) and log(base 2)(x^2) simplify to log(base 2)(x) + 1.
Hence, log(base 2)(x+2) = log(base 2)(x^2).