Math help (logrithms)?
462157
3^x = 10.4\n\nsince both sides are always positive, you can take the log of both sides...\n\nlog(3^x) = log(10.4)\nx*log(3) = log(10.4)\nx = log(10.4)/log(3)\n\nYou can use a calculator to figure out the log of 10.4 and 3.\n\nSteve
586612
remember your natural logs\n625^x = 1/125\nxln625 = ln(1/125)\nx = ln(1/125)/ln625 = -3/4
899135
1. Move the log part to the other side to make it positive, and move the 5 to the other side to get -2 = log(x+2)\nThe base of log is 10, so this means basically 10^-2 = x+2\n\n10^-2 is 1/100 or 0.01 = x + 2\n\n-1.99 = x\n\n2. 2e^(2x) + 5e^x - 3 = 0\n\nFactor by FOIL:  (2e^x - 1)(e^x + 3) = 0\n\nSo either e^x = 1/2 or e^x = -3 (which is impossible)\n\nYou can do ln (natural log) of both sides to "cancel out" the e:\n\nln(e^x) = ln (1/2) becomes x = ln(1/2)\n\n3. logx - 1/2log(x+4) = 1\n\nMinus becomes divide and the 1/2 becomes an exponent when combining logs.  So the left side simplifies to be:\n\nlog(x/(x+4)^(1/2))   Remember, 1/2 as an exponent means square root so this is\n\nlog(x/ sqrt(x+4)) = 1\n\nAgain, log has base 10 so this is really 10^1 = x/sqrt(x+4)\n\nSquare both sides: 100 = x^2/(x+4)\n\nCross multiply:  100(x+4) = x^2\n\n100x + 400 = x^2\n\nx^2 - 100x - 400 = 0  \n\nUse quadratic formula (be sure to eliminate negative answer(s) because you can't find the log of a negative number)
574891
im pretty sure that you will have to use the parts method to solve it. but the answer is\n\nx(log(1-ie^(ix))-log(1+ie^(ix))+i(Li(-ie^(ix)-Li(ie^(ix))\n\ni=imaginary unit\nlog=natural logarithm\nLi=polylogarithm\n\nyou can check my answer to see if its right because i also thought that it was wrong. i dont know how the imaginary units could have shown up but o well.
867514
[ 1/4 LOG (16) ] - [ 2 LOG (6) ] + [ LOG (3) ]\n\n[ LOG ((16)^(1/4)) ] - [ LOG ((6)^2) ] + [ LOG (3) ]\n\n[ LOG (2) ] - [ LOG (36) ] + [ LOG (3) ]\n\n...........................the first two LOGS have the same base of 10, \n...........................so when subtracting LOGS we divide.\n\n[ LOG (2/36) ] + [ LOG (3) ]\n\n[ LOG ((2divided by 2) / (36 divided by 2)) ] + [ LOG (3) ]\n\n[ LOG (1/18) ] + [ LOG (3) ] \n\n...........................the above two LOGS have the same base of 10, \n...........................so when adding LOGS we multiply.\n\nLOG ((1/18) times (3))\n\nLOG ((1/18) times (3/1))\n\nLOG (3/18)\n\n..................................then reduce the fraction by dividing by 3/3.\n\nLOG ((3 divided by 3) / (18 divided by 3))\n\nLOG (1/6)   \n\nLOG ((6)^(-1))\n\n..........an exponent can be moved and multiplied to the front of the LOG.\n\n(-1) times [ LOG (6) ]\n\n - LOG (6)\n\n\nTherefore, \n\n[ 1/4 LOG (16) ] - [ 2 LOG (6) ] + [ LOG (3) ] =     - LOG (6)
898977
log(2x+1)-(1/3)log(x+1)\n=log(2x+1) - log(  (x+1)^(1/3)  )\n=log( (2x+1) /   (x+1)^(1/3)  )
658763
Take the logarithm of both sides:\n\nlog a^a = log 2\n\nThen use the rule log (x^y) = y log x\n\nso a log a = log 2\n\nUnfortunately from here we can only solve numerically. Look at the graph of a log a and make approximations.\n\nThough not expressible using elementary functions, the actual answer is defined by the Lambert's W function and reads: log 2 / (LambertW (log 2)), which is roughly 1.5596. More about the W function and what it's used for below.
1046114
80=16*5\n\nlog(2^4*5)/log2\n=(log2^4+log5)/log2\n=(4 log2+log(10/2))/log2\n=(4log2+log10-log2)/log2\n=(3log2+1)/log2=3+(1/log2)
725458
Hello dear Sherri \n\n● 4^(2x+1) = 2^(3x+6)\n-Take ' log ' from each sides\n\n● log [4 ^ (2x+1)] = log [2 ^ (3x+6) ]\n● (2x+1) log 4 = (3x+6) log 2\n   { as you know you can get log 4 =  2 log 2 }...\n● 2(2x+1) (log 2) = 3x+6 (log 2)\n   { cancel " log 2 " } ...\n● 4x+2 = 3x+6\n- Now its a simple function \n● 4x - 3x = 6 - 2\n● x = +4\n\nGood Luck Darling ♣
902324
Hello dear \n\n▪log ( x +3 ) + log (x) = 1 \n{ as you know if base is a so log (xy) = log x + log y }\n▪log x(x + 3) = log 10 \ncancel " log " \n▪x(x+3) = 10 \n▪x ² + 3x - 10 = 0\n▪(x + 5)(x - 2) = 0\n▪x = + 2 \n▪x = - 5  { cant accept it ,  because 0 < a = b   <=>  log a = log b }\n\nGood Luck.
1093339
No one on here is going to actually DO your homework for you.. but here is a place for you the get help -\n\nhttp://www.themathpage.com/aPreCalc/logarithms.htm\n\nhttp://en.wikipedia.org/wiki/Logarithm\n\nhttp://physics.mtsu.edu/~wmr/log_2.htm
1128770
You want to exponentiate your logarathim. For example, a=log x is the equivalent of 10^a=x.\n\nIn your problem, first multiply both sides by negative one to move the negative sign to the other side. Then, -6.00=log[OH-] becomes 10^(-6)=[OH-]. Your concentration of OH- is 10^-6 M.
360289
The correct answer is:   (12 / a) - 4\n\nThis can be checked by a = log 216/log 12 = 2.163\nlog 16/log 6 = 1.547\n12 / a - 4   = 1.547\n\nSolution method:\nNote that log(6)16 = log(6)2^4 = 4log(6)2\nSo if we can get log(6)2 in terms of "a" we can find our solution.\n\na =\n= log(12)216\n= log(12)6³\n= 3 log(12)6\n= 3 log(6)6 / log(6)12 ...........by change of base\n= 3 / log(6)12 ......................by log(6)6 = 1\n= 3 / (log(6)2 + log(6)6) ........by log ab = log a + log b\n= 3 / (log(6)2 + 1) ................by log(6)6 = 1\n\nRearrange \na = 3 / (log(6)2 + 1) \n\nto give\nlog(6)2 = 3 / a - 1\n\nThen\n\nlog(6)16 = 4 log(6)2 = 4 ( 3 / a - 1) = 12 / a - 4
82029
it's a simple work: I'll give you a suggestion, but you should try to do it by yourself.\n\ny intercept: you find it by setting x=0 so you get\n\ny= log(base2)(2) + 3\n\nThe logarithm is simple to calculate ---> get an integer answer.\n\n---\n\nx intercept: you must set y=0 this time.\nYou get the logarithmic equation\nlog(base2)(x+2) = 3 ---> to solve for x, let each member be the exponent of a power with base 2:\n\n2^(logbase2(x+2)) = 2^3\n\n---> use definition of logarithm (why did we choose a power with base 2?) and get to an integer solution.\n\nGood work.
496208
log(x) - log(1 + (x^2 + 1)^(1/2))\n\nWhere log is the natural logarithm, of course.
178809
Have you considered some sort of logarithmic compression?  for example, 10*log10(x+1)\nthen 10*log10(1+1) = 3\n10*log10(3+1) = 4\n10*log10(2+1) = 3.7\n10*log10(2.5+1) = 3.?\n10*log10(400 +1) = 26\n10*log10(500 +1) = 27\n\nother types are possible using the natural instead of the base 10 log.   there may be some rounding errors in my numbers, i wasn't using a calculator.\n\nI hope I didn't misunderstand your qustion.
689473
get the n's on one side\nso\n17959/21558=(1.02/1.03)^n\nor\n.833055014=.990291262^n\nusing logs with change of base\nn=log (.833055014)/log(.990291262)\nor n=18.72