im expanding log7(7x) and not getting the right answer which is 1+log7x.  How do you get this answer?im lost?
470727
log_7(7)+log_7(x)=1+log_7(x).
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)
855011
log[4]a = k, where [4] is the base.\n\nTherefore, a = 4^k\n\nNow take the log of both sides to the base [a].\n\nlog[a]a = k * log[a]4\n\n1 = k * log[a]4\n\nlog[a]4 = 1 / k\n\nThis is not quite the same as you have, so have you asked to solve the correct expression?\n\nIf, from a = 4^k, you take the log to base [k], it becomes :\n\nlog[k]a = k * log[k]4\n\nSo, log[k]4 = log[k]a / k, instead of your answer 1/ k.
780572
First let's remember some rules of logs.\nThe log of product is the sum of the logs.  That is,\nlob(a*b) = log(a) + log(b)\nThe log of a quotitent is the difference of them.  That is, \nlog(a/b) = log(a) - log(b)\nAnd finally, if you have an exponent, you can bring it in front of the log.\nlog(a^n) = n*log(a)\nRemember that you can only take the log of positive numbers.\nln[ x^2 / [sqrt(x) (2+x)^2] ]\n= ln(x^2) - ln[ sqrt(x) (2+x)^2]\n= 2ln(x) - [ln(sqrt(x)) + ln(2+x)^2]\n= 2ln(x) - (1/2)ln(x) - 2ln(2+x)\nYou can combine 2ln(x) - (1/2)ln(x)\n2ln(x) - (1/2)ln(x) = (2 - 1/2)ln(x) = (3/2)ln(x)\nAnswer: (3/2)ln(x) - 2ln(2+x)\nNote: sqrt(x) = x^(1/2)
470800
logx 1/a = (logx 1) - (logx a)\n= 0 - 3\n= -3
574441
I get\n10.10110111111...\n\nThe question is essentially asking for the value of e in binary. This is no the same as log_2(e). The answer should only have 0 and 1's.
387252
x = log(7)19\n\n7^x = 19\n\nx = (log19)/(log7)\nx = about 1.513
824419
log 10 * log 10 = 1 because log (base 10) 10 = 1 \nand therefore 1 * 1 = 1\n\nlog 10 + log 10 = 1 + 1 = 2 \nand log 10 + log 10 = log (10*10) = log 100\nlog 100 = 2 means 10^2 = 100 noting again that log means log (base 10) meaning it is the power to which the base is raised to get its argument\n\n1000 = 10^3 so log 1000 = 3\n\nNow using the rules stated\n[ie  log a - log b = log (a/b)\nlog a + log b = log ab\nlog a^b = bloga]\n\nlog 3 + 3 log y = log3 + log (y^5) (since bloga = log a^b)\n= log(3 * y^5) (since log a + log b = log ab)\n= log (3y^5)\n\nThe log of a product = the SUM of the individual logarithms!\n\nlog(ab) = loga PLUS logb defintely NOT loga TIMES log b
533385
Please believe TheoDorkx. He's the only one who understands logarithms.\n\nAnother way to solve logarithm problems is directly change from the logarithmic to the exponential form.\n\nln(2x) = 2 means that 2 is the power to which you raise the base of the logarithm, e, in order to get the result 2x.\n\nSo the equivalent exponential form is\n\n2x=e^2\n\ntherefore\n\nx=(1/2)e^2\n\nThis is the same thing TheoDorkx got with his approach. I offer it as a slightly different way to think about the problem.
978753
log 3x = log 5 + log (x-4)\nlog 3x = log 5(x-4)\n10 ^ (log 3x) = 10 ^ (log 5(x-4))\n3x = 5(x-4)\n3x = 5x - 20\n-2x = -20\nx = 10\nAnswer checks out.
881075
if these are decimal logarithms, i.e. log base 10, use the formula\n\nlog(ab) = log a + log b\n\nfor example,\n\nlog(417) = log (4.17 * 100) = log 4.17 +log100\n= .6201 + 2\n=2.6201\n\nlog0.417 = log 4.17 + log0.1 = .6201 -1 = -0.3799\n\nlog(.1) = log (10^(-1)) = -1
350639
7^(2x + 1) = 3^(x + 2)\nlog(7)(x + 2) = log(3)(2x + 1)\nIn the second step, you switched the x+2 and 2x+1\nLine 2 should be\nlog(7)(2x + 1) = log(3)(x + 2)\nContinue solving as you did before and you will get the correct answer.\n\nAlso, you wouldn't write ln9 just because it is not in simplest form\nln(9) = ln(3^2) = 2ln(3)\nSimilarly for ln(49) = 2ln(7)
496208
log(x) - log(1 + (x^2 + 1)^(1/2))\n\nWhere log is the natural logarithm, of course.
808044
Take the log of both sides:\nlog(0.01) = log(2.2^-t/8)\n\nRemember that log(a^b) = b * log(a), so bring the -t/8 in front:\nlog(0.01) = -t/8 * log(2.2)\n\nNow just solve algebraically:\n-t/8 = log(0.01) / log(2.2)\nt = -8 * log(0.01) / log(2.2)\n\nlog(0.01) = -2\nlog(2.2) ≈ 0.342422681\n\nt = (-8 * -2) / 0.0.342422681\nt = 16 / 0.342422681\n\nTherefore:\nt ≈ 46.7258768\n\nAs a double check, you can plug it in your calculator:\n2.2^(-46.7258768/8) = 0.01
708168
alog(x) = log(x^a)\n\n1/4log_b(16) = log_b(16^1/4) = log_b(2)\n\n2log_b(5) = log_b(5^2) = log_b(25)\n\nlog_b(7) doesn't change.\n\nlog(x) + log(y) = log(xy)\n\nand \n\nlog(x) - log(y) = log(x/y)\n\nTherefore\n\nlog_b(2)-log_b(25)+log_b(7) = log_b(14/25)
703752
simply subtract 7 from both sides. This leave you with\n\nx<_3
7970
Log(a^b)= b*Log(a)\nLog(ab) = Log(a)*Log(b)\n\na) Log147= ?\n147= 3*7*7\n=> Log147= Log3 * (Log7)^2\n=> Log147= 2yw\n\nb) Log28= ?\n28= 2*2*7\n=> Log28= (Log2)^2 * Log7\n=> Log28= 2xw