<p>(5^x)+(9^x)=92
solve for x
someone please explain this in detailed steps.
thanks</p>
<p>no one can answer this???</p>
<p>xlog5 + xlog9 = log92
x(log5+log9) = log92
x = log92 / (log5+log9)
x= 1.1879</p>
<p>better still log5 + log9 = log(5 x 9) = log45
so x = log92/log45
yep, Dieselboy is right.</p>
<p>Not actually correct, DeiselBoy, 'cause 5^1.1879 + 9^1.1879 = 20.366</p>
<p>You can't take the log of each item on the left side of the equation...you have to take the log of the whole side...but that doesn't seem to help...</p>
<p>the answer is algebraically correct. this simply implies that the question is wrong.</p>
<p>you can take the log of each item. but when you take the log of the whole side, it becomes xlog(9 x 5) or log(9^x x 5^x) = xlog45</p>
<p>No, you can't. For example, if you have 2 + 3 = 5, you can't say log(2) + log(3) = log(5). That would simplify to log(6) = log(5) by your reasoning.</p>
<p>So, if you take the log of both sides of the previous equation, you get log( (5^x) + (9^x) ) = log(92). That, unfortunately, doesn't seem to help.</p>
<p>If you graph the original equation, you can get an approximation of 1.6xxx</p>
<p>obviously not! taking log of both sides whichever way, one needs to observe simple laws of logarithms. so log2 + log3 = log(2 x 3) = log6 [that's a law].</p>
<p>Right, that's my point.. So your solution, which requires taking the log of each item on the left and the entire right side doesn't work.</p>
<p>yeah, then this is a somewhat difficult question.</p>
<p>Definitely. Still trying to figure out how do do it without graphing...</p>
<p>yeah. this hard nut must be cracked. will soon be.</p>
<p>Just FYI, if you graph the curve y=5^x +9^x and the line y=92, and then solve for the intersection, you get a nice approximation of x: 1.62848..... but I still want someone to figure this one out. :)</p>
<p>the key is to convert 5^x to a multiple of 3^x so you can obtain a quadratic equation putting p = 3^x. then when you solve for the real value of p, you can now get x by: x = logp/log3.</p>
<p>i've tried this problem my last two class periods, still can't crack it. it may not be algebraically possible. my ti89 solved it, but i think it only guesses and checks really quickly.</p>
<p>This problem cannot be solved with logs or anything like them. You cannot solve for x algebraically; you have to use a graph or a more advanced calculus-based method.</p>
<p>yeah, just like pete said plot y = 5^x + 9^x and y = 92 and find the point of intersection. you could also use numerical methods. keep substituting for x until you get a change of sign.</p>
<p>by numerical methods, 1.931 < x < 1.932</p>
<p>you have to make it so that 5 and 9 have the same base.. but i dunno if this is even possible. I'd just graph it.</p>