log base2(10) = 5 since 25 ≡ 10 (mod 11)\nthis is an example that was given by my professor... I don't understand it.  \npage 6 on the following link\nhttp://orion.math.iastate.edu/sysong/S06/M533/LectureSlides/L-31.pdf
202210
Hiya, right here goes - \n\nyou want to find log10 . where log is to the base 2.\n\nfrom the prvious lecture notes you can see that the starting point fot the discrete logarithm is to fix a primative element which is dependent on which base you are working to. By definition this is an element g such that\n\ng^i ≠ 1 (mod p) for 1<i<p-2  ( and p>10 for it to work)\n\nin the example g=2 and p=11. p has been chose as 11 because\n\n 2^i ≠ 1 (mod p)  for 1<i<9\n\nhe point of the logarithm is then to find i such that 2^i ≡ 10 (mod p) trial and error gives that 2^5 ≡ 10(mod 11)\n\nso log10=5
227156
log(x) - log(1 + (x^2 + 1)^(1/2))\n\nWhere log is the natural logarithm, of course.
555844
2^(x+1) = 5^(1-2x)\n\nlog 2^(x+1) = log 5^(1-2x)\n\n(x+1) log 2 = (1-2x) log 5\n\n(log 2 + 2 log 5)x = log 5 - log 2\n\nx = (log 5 - log 2)/(log 2 + 2 log 5)
55752
The other property of logarithms is that Log_x A - Log_x B = Log_x (A/B)\n\n\nso you can combine this rule with the other one i told you about in your other question...\n\nthe only thing is that u are working in reverse order\n\n\nLn 2y/x= Ln 2+ Ln y - Ln x\n\n\nThese are properties, they should be tought to you as principals, without them you cant solve logs:D hope this helps ;) if you think it does pls gimme 10 pts:P
402804
OK, there's 2 possibilities:\nIf you meant:\nlog (16^1/4), then you need to know the property of logarithms where:\nlog a^b = b log a.\n\nSo:\nlog 16^(1/4) = 1/4 log 16\nlog 10^(.01) = .01 log 10\nlog 2^(1/8) = 1/8 log 2\n\nIf you meant (log 16)^1/4, then I have no idea how to do it by hand.\n\nEdit:\nFurther, you can also do things like:\nlog 16 = log 2^4 = 4 log 2\nso 1/4 log 16 = 1/4 * 4 log 2 = log 2.
346114
I'm sure you must have been given these few principles of log operations:\n1. log a + log b = log ab\n2. log a  - log b = log (a/b)\n3. log a^p          = p*log a\n4. log 1 = 0\n5. log (subscript b) b = 1\n\nIn the first problem, if you apply rule 3 it becomes\n1/5(log(x+1)^3 + log(x-1)^2 - log 7), then apply rules 1 and 2 and you get\n1/5log(((x+1^3)*(x-1)^2)/7), a horrible looking expression and I don't know why anyone would ask you to touch it!\n\nIn the second one, log (subscript b) x*b\n= log x + log b [by rule 1]\n= log x + 1     [rule 5]\nTo deal with log sqrt 10, remember \nsqrt 10 = 10^(1/2) and use rule 3;\nalso 10 = 2*5 and use rule 1 in reverse, i.e. split log 10 into log 2 and log 5.\n\nI can't do much more without actually doing them all for you, and I don't think I should do that.\n\nIn  problem 3, take the log of each side and use rule 3, i.e.\nto solve  a^(x + b) = c, do\nlog a^(x + b) = log c\nand then (x + b)*log a = log c\n\nYou can';t do q.4 without knowing what the base of logs is.  I'd assume it's 10 and use rule 1 and solve\nlog x(x+3) = log 10\n\nIn problem 7, I think those 4's are all subscripts, in that case you are right and have used the rule I omitted: \n\nlog (subscript b) x  = (log x)/(log b)\n\nHowever, if you apply rule 3 to log 64, using 64 = 4^3, you'll simplify your answer a great deal.  Is it 3?
462950
When we need to ind the logarithms of number not of base ten, we can use log*6*x=logx/log6 so the answer is\n(log60)/(log6)-(log30)/(log6)
300997
you can change the base...\nln x = (log2 (x))(ln 2)
252407
it is a proving isn't it?\nright handside: [logbase10 1000]/logbase10 2\n=[logbase10 10^3]/[(logbase2 2 )/( logbase2 10)]\n=3[logbase10 10]x[logbase2 10]\n=3logbase2 10\n=logbase2 1000 , proved\n\n\n\nif its right do mark it best i'll come to know i have done correct or not.\nsorry here is the right answer\nanswer is 4\ni got it by\nlogbase2 1000=1ogbase10 1000 / logbase100 "x"\n3logbase2 10=31ogbase10 10 / logbase100 "x"\nlogbase2 10=1/logbase100 "x"\nlogbase100 10 / logbase100 2 =1/logbase100 "x"\n.5logbase100 100 / logbase100 2 =1/logbase100 "x"\n2logbase100 2=logbase100 "x"\nlogbase100 2^2=logbase100 "x"\n2^2="x"\n"x"=4
103739
The short answer is, you don't.\n\nThe log is the exponent you put on the base to get the number you want the log of.  base 10 log of 100 is 2, because 10^2=100.  But all powers of 1 are 1, and all powers of 0 are 0.
549032
log(base a) b = logb/loga.\n\nSo take the log of X and divide by the log of 1/3.  Then press the +/- button because you're being asked for the negative of that value.
490094
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)
490095
2log(base3)x-log(base3) (x-4) = 2+log(base3)2\nlog_3 x^2/(x-4)=log_3 9+log_3 2=log_3 18\nx^2/(x-4)=18\nx^2=18x-72\nx^2-18x+72=0\n(x-12)(x-6)=0\nx=12\nx=6
318748
Yes, there is a formula to change the base of a logarithm, and here it is...\n\nIf you have an expression log(x) with base 3, the change of base formula allows you to re-express this in the form (lg x)/(lg 3), where lg refers to a logarithm with a base of 10.\n\nFor information on the change of base formula and other logarithmic rules, you may find this page useful:--\nhttp://en.wikipedia.org/wiki/Logarithmic_identities
127485
log base 2 of 10,000 is log base 10 of 10,000 divided by log base 10 of 2, that's 4/0.3010 = (without a calculator) 13 or so.  13.29.
338831
Log(x + 2) + Log(x - 1) = Log(70)\nAs I explained before,\nLog (a0 + Log (b) = Log(ab)\nSo,\nLog(x + 2) + Log(x - 1) = Log [(x + 2)(x - 1)]\nLog [(x + 2)(x - 1)] = Log(70)\n(x+2)(x-1) = 70\nx^2 - x + 2x - 2 = 70\nx^2 + x = 72 \nx^2 + x = 72\nx^2 + x - 72 = 0\nx^2 - 8x + 9x - 72 = 0\nx(x - 8) + 9(x - 8) = 0\n(x + 9)(x - 8) = 0\nNow, either x + 9 = 0 or x - 8 = 0\nIf we put x + 9 = 0, we get x = -9\nIf we put x - 8 = 0, we get x = 8\nBut when we substitute x = -9 in the original problem we get Log (-7) + Log (-10) = Log(70)\nBut Log of negative numbers if undefined.\nSo, x = 8 is the only solution.
254518
1. 6^(-.2x)=10\n(-.2x)ln(6)=ln(10)\nx=-5*ln(6)/ln(10)\n\n2. 7log_5(x)=18\nlog_5(x)=18/7\nx=5^(18/7)