<p>It's going to be my first time taking the ACT tomorrow, and I'm also taking writing. But what I really need help with (right now) is math. This is a person who gets 60s on her math tests, okay? Please dumb down your explanations and be patient with me :)</p>
<p>a) log(subscript of 3)36 - log(subscript of 3)4 = log(subscript of 8)X</p>
<p>Find X. The answer is supposed to be 64.</p>
<p>Please include the steps taken in plugging numbers into the calculator if you can. </p>
<p>b) ((square root of 36) ^(-1/4)) </p>
<p>c) If g(x) = 4x^2 + 6x - 9, what is g^(-1)(79)?</p>
<p>d) x^(3)y^(-2)z * (xy^(2)z^(-3))^(-2)</p>
<p>e) What do you say is an acceptable composite score? This is my first and last chance to take it so I must do good.</p>
<p>b) Well, the square root of 36 is 6. So you’re looking at 6^(-1/4), which can just be plugged into your calculator. It doesn’t come out neat, and since you don’t have answer choices I’m not sure what they want you to find. But 6^(-1/4) is the same as 1/6^(1/4).</p>
<p>e) An acceptable score really depends on what colleges you’re applying to.</p>
<p>a) This question can be done completely on your calculator. Since your calculator only uses the log of 10 naturally you need to turn each log into a fraction to get a whole number. </p>
<p>log(sub 3)36= log36/log3 =3.26…</p>
<p>log(sub 3)4= log4/log3= 1.26…</p>
<p>If you cursor up to the numbers that the calculator produced and subtract 3.26…-1.26… you should get a whole number of 2. </p>
<p>Now you need to plug this in. </p>
<p>We now know that log(sub8)X=2</p>
<p>(You need to memorize this) This would then be the same if written as 8^2=X</p>
<p>8*8=64</p>
<p>If g(x) = 4x^2 + 6x - 9, what is g^(-1)(79)?</p>
<p>remember that for whatever value of x in the first equation, you must get 79 as the solution to the first equation since they g(x) and g^-1(x) are inverses. additionally, remember that for an x value of 79 in the 2nd equation, you must get the value of x in the first equation as an answer since they are inverses.</p>
<p>knowing this, take 79 and plug in for g(x) and factor it out. You should get x=4, x=-11/2. they should be the correct answers, because if you take g^-1((g(x)) or g(g^-1(x)), and plug in those values you solved for, you should get 79 as an answer.</p>
<p>a) You don’t need a calculator for this one. There is a nice property of logarithms that says that log a - log b = log(a/b). Here,</p>
<p>log<em>3 (36) - log</em>3 (4) = log<em>3 (36/4) = log</em>3 (9) = 2.</p>
<p>Here, we’re just solving log_8 (X) = 2. Hence, X = 8^2 = 64. ∎</p>
<p>b) That’s just 6^{-1/4} or 1/(6^{1/4}). Use your calculator. ∎</p>
<p>c) I don’t think g has an inverse “function” but intuitively, g^(-1) (79) would be the x-value that yields g(x) = 79. So you have 4x^2 - 6x - 9 = 79, use the quadratic formula. ∎</p>
<p>d) Order of operations, do the (parentheses)^(-2) first. The way you wrote it is a little ambiguous (don’t worry, it’s difficult to type them in unless you know LaTeX or another typeset font) so I won’t solve it. ∎</p>
<p>e) Average score is around 21, but an “acceptable” score depends on the college you’re applying to, just like iluvbooks94 said. ∎</p>