Could you please verify and calculate the following logarithmic equation:

y = 2log_2(2)(x+2)-4 , in which x=2.
So the equation would become:
y = 2log_2(2)(2+2)-4
Solving...
y = 2log_2(2)(4)-4
y = 2log_2(8)-4
y = 2(3)-4
y = 6-4
y = 2

So I got y=2, however my answer sheet and my graphing calculator when I typed in the equation gave me y=4. How is this and where did I miscalculate?
Please note: that the "_" means subscript.

I will read your equation as

y = 2log2 (2(x+2)) - 4
so when x = 2 , we have
y = 2log2 (8) - 4 , so far the same as yours
y = 2(3) - 4
= 2

We seem to agree based on the way you typed the question.

Just tried different combinations of your typing ...

if you meant

y = 2log2 2^(x+2) - 4

then
y = 2log2 2^4 - 4
= 2log2 16 - 4
= 2(4) - 4
= 4

Thank you. I actaully just figured out that I indeed had miscalculated the equation. It was: y = 2log_2(2) (x+2)-4

Therefore I should solve the "log" part first:
1) y = 2log_2(2) (2+2)-4
2) y = 2 (2+2)-4
3) y = 2 (4)-4
4) y = 8-4
5) y = 4

In other words, the number "2" just before "x" applied to the 2log_2 and was not supposed to be multiplied with the (2+2) until the second step.

No, wait, actually the 2 does not apply to the 2log_2 by itself. Rather, the "2(x+2)" applies to the log. I was so confused, sorry. So I'm going to assume that the answer "2" is correct and the "4" on my answer sheet is incorrect.

To verify the calculation, let's break down the process step by step:

Starting with the equation:
y = 2log₂(2)(x + 2) - 4

Given that x = 2, we substitute it into the equation:
y = 2log₂(2)(2 + 2) - 4

Simplifying within the parentheses:
y = 2log₂(2)(4) - 4

Next, we simplify the logarithmic expression:
log₂(4) = log₂(2²) = 2log₂(2)

Substituting back into the equation:
y = 2 * 2log₂(2) - 4

Now, we evaluate the 2log₂(2):
2log₂(2) = 2 * 1 = 2

Substituting this value back into the equation:
y = 2 * 2 - 4
y = 4 - 4
y = 0

Based on the calculations, it seems there was an error when evaluating 2log₂(2). The correct value should be 2, not 1. Therefore, the correct answer is y = 0, not y = 2.

It's possible that the error occurred during calculations or when entering the equation into the graphing calculator. Please recheck the steps and ensure that the correct logarithmic value is used.

Additionally, make sure to input the equation accurately into the calculator, including the logarithmic base and any necessary parentheses to avoid ambiguity.