convert to exponential form:     log (subscript)5  625  =  4?
815187
5^4=625\nsubscript is the base number, the answer is the exponent, and the regular number after the log (sorry can't remember the name) is the answer.
496208
log(x) - log(1 + (x^2 + 1)^(1/2))\n\nWhere log is the natural logarithm, of course.
630919
all you have to do is use the change of base formula:\n\nlog5/log12=.6477
290613
The sum of the logs is the log of the products, ie.\nlog(a)+log(b)=log(ab)\n\nSo combine the sum of logs here into a single log of the product of (x-3) and (x+3).\nlog_4(x-3)+log_4(x+3)\n  =log_4((x-3)(x+3))=2\n\nOnce you have a single log isolated on one side of the euqation you should remember that the log equation log_a(b)=x is equivalent to the exponential equation a^x=b, so in this case\n(x-3)(x+3)=4^2=16\n\nNow you've got a quadratic equation that you can solve for x by expanding everything, moving everything to one side of the equation, and factoring.\nx^2-6x+9=16\nx^2-6x-5=0\n(x-5)(x-1)=0\nx=1 or 5\n\nYou should then check to see if both of these solutions are valid in the original equation. Since letting x=1 would involve taking the log of a negative number in the original equation (which you cannot do if you are dealing with real numbers) you should throw that solution out.\n\nx=5
962408
log4+xlogb=xloga\nx(loga-logb)=log4\nx=log4/(loga-logb)
477145
log(2x+1) - log5  = log x\nlog(2x+1) - log x = log 5\nlog((2x+1)/x)  = log 5\n(2x+1)/x  = 5\n2x+1 = 5x\n3x = 1\nx= 1/3
815091
First of all, we apply the power rule:  a*log(x) = log(x)^a\n\n     2*log(a(x+1)) = log(a(x+1))^2\n\nNext, we know that the sum of two log expressions can be written as a single product: log(a) + log(b) = log(a*b)\n\n     log(a(y+5)) + log(a(x+1))^2 = log[a(y+5)*(a(x+1))^2]\n\nYou may try some algebraic simplification, but I think that these concepts are the ones that are being tested for this problem.
795919
log a (7x+1)=log a (4x+16)\n7x+1= 4x+16\n3x = 15\nx= 5\n`
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
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 ♣
636548
e^(3x)=4\n\n3x[log(e)]=log4\nx=[log4]/[3*log(e)]\nx=[ln4]/3\n\nanother solution is to convert e^(3x)=4 to log form directly...if you do that you'll get:\nln4=3x and then transpose the 3...
932114
So you have the formula, and you have the number to plug into it. Are you confused about how to deal with the exponents? \n\nIntensity = 5.4 x 10-10, so\n\nd= 10 * log( 5.4 x 10-10/ 10-12)\nd= 10 * log(5.4 / 10-2 )  \nd= 10 * log(540)\n\nd= 10 * 2.732                        note it is a base 10 log!!\nd= 27.32
246299
h= (C*I/A+T/k)*z*log(.7*y)
19421
X^5 = 98\n=> ln(X^5) = ln98\n=> 5lnX = ln98\n=> lnX = (ln98)/5\n=> X = e^((ln98)/5)\nX = 2.50175752714084352...
956834
For log(x+8) to be log x +log 8 ,x+8 must be equal to 8x\nWe can write it algebrically as log(x+8)=logx+log8=log(8x)\n=>8x=x+8\n=>7x=8    or,x=8/7
437664
The secret is to understand some of the rules of logarithms and adjust translate the numbers to make your lob easier.\n\nThe rules:\nlog(a*b) = log(a) + log(b)\nlog(a/b) = log(a)- log(b)\nlog(a^n)=nlog(a)\n\nIf I understand your problem:\n\nx= [(86400)*sqrt(365.25)]/[ (.079)^11]\n\nso log(x) = log [.....]\n\n     = log(86400)+log(356.25^.5) - log(0.79^11)\n     = log(86400)+.5*log(356.25) - 11*log(0.79)\n\nuse log tables to get the logs and add them up to get the log of x.  Use the tables again to find x.\n\nYou can make other approximations, i.e., 356.25 is close to 19^2 (=361)\nand 86400 is close to 300^2 (=90000) and continue from there.  \n\nHope that helps.
586612
remember your natural logs\n625^x = 1/125\nxln625 = ln(1/125)\nx = ln(1/125)/ln625 = -3/4