<p>what is x in this problem:</p>
<p>2 X 3<strong>x = 8 X 7</strong>x</p>
<p>When i say 3**x I mean 3 to the power of x</p>
<p>I am totally stumped thanks</p>
<p>Which math SAT? The SAT I? It seems too advanced. It's been a few decades for me, but I'd think you'd need natural logs (x = ln 4/ln(3/7)) or x = -1.636135...). I don't think I came across problems like that until calculus - but it might have come up earlier, I just can't remember. I think it would be easier to do some trial and error attempts with your calculator - was this a multiple choice question?</p>
<p>Hopefully, my memory still works after 20+ years - it;s not the sort of problem I have to think about every day.</p>
<p>heres the solution to that:</p>
<p>2 * 3^x = 8 * 7^x</p>
<p>3^x = 4 * 7^x</p>
<p>log base 3 of (4*7^x) = x
log base 3 of (4) + log base 3 of (7^x) = x</p>
<p>(ln 4/ln 3) + x(ln 7/ln 3) = x</p>
<p>1.26185 + x(1.77124) = x</p>
<p>.77124x = -1.26185
x = -1.63613</p>
<p>There ya go.
just use log properties, change of base formula and log addition rules.</p>
<p>hope u understand my work here.</p>
<p>worry not - no logs on SAT I.
eg1's way is a bit faster.
3^x/7^x=4
(3/7)^x=4
x= log(base 3/7) 4 =ln 4/ln(3/7)</p>
<p>ti-89 is the solution to life</p>
<p>solve(2<em>3^x=8</em>7^x,x)</p>
<p>x= -2ln(2) / ln(7/3)
x~ -1.636</p>
<p>You don't need a TI-89, TI-83's or 84's do one-variable algebra just as well...
Here's how to do it with a TI-83+
Hit the "y=" button.
Put one side of the equation next to Y1 and the other side next to Y2.
Make sure you don't have other equations in there and make sure the "=" next to Y1 and Y2 are lit up.
Hit "2nd", then "TRACE". Scroll down to INTERSECT (or hit "5").
Press "ENTER" 3 times.
Presto, you get the value of x.</p>
<p>If you're not used to it it's a little time-consuming, but it's great if you're stuck.</p>
<p>ListedMIA's way is how most people would do it.</p>
<p>this would be in a math IIC test. If it were a math SAT 1, then the answer would be somthing simple like 1 or 2...anyways, get a ti-89 for math IIC to save time.</p>
<p>I love the solve() fxn! Thank you very much, TI-89.</p>