Math Help - Exponents

<p>1.</p>

<pre><code> If 2^x + 2^x + 2^x + 2^x = 2^7, what is the value of x?
</code></pre>

<p>What I did was 2^4x = 2^7, but that is wrong, and it's supposed to be 4 * 2x, but I don't understand the exponent rule for this. Could someone please explain it to me?</p>

<p>2.</p>

<pre><code> If x and y are positive integers and 4(2^x) = 2^y, what is x in terms of y?
</code></pre>

<p>A. y - 2
B. y - 1
C. y
D. y + 1
E. y + 2</p>

<p>Is it possible for me to multiply the 4(2^x) by doing 8^x? Or can I not do that because the 4 does not have an exponent? Could someone, again, please help me to understand the rule behind this?</p>

<p>2 ) 4(2^2) = 16. In which case, X = 2.
2^y = 16, in which case, Y = 4.
What is X in terms of Y? 2 = 4-2, therefore X = Y -2. Choice A.
See how substitution makes math that much easier and more approachable?</p>

<p>Here is a quick review of rules:
A^X times A^Y = A^X+Y -> 2^2 times 2^3 = 2^5
(A^X)^Y = A^X times Y -> (2^2)^3 = 2^6
A^X + A^Y does not apply to any exponent rule.
A^X - A^Y does not apply to any exponent rule either.</p>

<p>For number 1, the correct solution would be to simplify the equation to 4(2^X) = 2^7, and then solve it, through the shift+solve option on the calculator (which I prefer, since it's more time friendly), or through regular math.</p>

<p>1) 2^x + 2^x + 2^x + 2^x = 4<em>(2^x)= (2^2)</em>(2^x) you add the exponents now= 2^(2+x)= 2^7</p>

<p>2+x=7.... X=5 ( you can only add exponents when the numbers are being multiplied, so that's what I did- I turned the adding into multiplication and changed 4 to an exponent of 2 in order to add exponents)</p>

<p>2) 4(2^x) = (2^2)*(2^x) add the exponents= 2^(x+2)= 2^y..... x= y-2 (No, you can only do that if the two numbers have the same exponent. Besides, why would you do that? The left side of the equation is telling you that the base needs to be 2! )</p>

<p>Learn to spot exponents. If don't understand the rules of exponent, use this link: Exponents:</a> Basic Rules.</p>

<p>Ooops, I didn't notice that somebody else already answered. Sorry!</p>

<p>
[quote]
If 2^x + 2^x + 2^x + 2^x = 2^7, what is the value of x?

[/quote]
</p>

<p>4(2^x) = 2^7; 4 is equal to 2^2
2^2(2^x) = 2^7; Divide both sides by 2^2
2^x = 2^5;
x = 5</p>

<p>
[quote]
If x and y are positive integers and 4(2^x) = 2^y, what is x in terms of y?
A. y - 2
B. y - 1
C. y
D. y + 1
E. y + 2

[/quote]
</p>

<p>For this problem, You need to understand that (a^b)/(a^c) = a^(b-c).</p>

<p>4 is the same as 2^2. Therefore, divide both sides by 2^2 and you get....
2^x = 2^(y-2)</p>

<p>x = y-2</p>

<p>wait I'm most likely missing some basic exponent rules here myself...</p>

<p>in the first problem, if you did the multiplication 4(2^x), you do end up with 8^x, right? or...</p>

<p>4(2^x) does not equal to 8^x because you cannot combine the bases like that if the exponents are different. It should be (2^2)(2^x)=2^(x+2)</p>