I need help w/ these problems...2^2x-18*2^x+32 solve for x and log x(x+5)^ 2 simplify?
926368
2^2x-18*2^x+32 = 0 (I assume)\nLet y = 2^x\nThus 2^(2x) = y²\n\nSo y² - 18y + 32 = 0\n(y - 16)(y - 2) = 0\nSo y = 2 or 16\n= 2^1 or 2^4\nSo 2^x = 2^1 or 2^4\nie x = 1 or 4\n\n\nlog x(x+5)^ 2\n= log x + log(x+5)^ 2\n= log x + 2 log(x + 5) \n(Using log (XY) = log X + logY and log (Yª) = alogY)
399499
x=2 and A=5/8 so sub2 = 1 and 1/4\nFirst we solve for X\n20 * x^4 = 320\nx^4 = 16\nx = 2\n\nThen we solve for A\n2^5 * A = 20\n32 * A = 20\nA = 20/32\nA = 5/8\n\nThen we go back and plug it in to sub 2\n5/8 * 2 = 10/8 or 1 and 1/4
880448
ln(x+6)-ln5=ln(x+6)/5  difference rule\nln(x+6)/5=ln(2x-7)  given\nsince the logs are equal removing the log sign\n(x+6)/5=2x-7\nmultiplying by 5\nx=6=5(2x-7)\nx+6=10x-35\nadding -6\nx=10x-41\nadding-x\n0=9x-41\nadding 41\n9x=41\ndividing by 9\nx=41/9
911082
logx+log(x+48)=2\n=>log{x(x+48)}=2\n=>log(x^2+48x)=2\n=>x^2+48x=10^2\n=>x^2+48x-100=0\n=>x^2+50x-2x-100=0\n=>x(x+50)-2(x+50)=0\n=>(x+50)(x-2)=0\nhence,\nx=-50 or x=2
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Since this is college algebra, it should be tough, but I'm having reading errors on the problem.\n\nCan't you just simply it down?\n\n8.5 = log (B/10^-16)\n\n10^8.5 = B/10^-16\n\nB = 10^-7.5
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log2 8 = 3, because 2^3 = 8\n\nlog 4 8 = x, then 4^x = 8.  4 is 2^2, so 4^x = 2^2x = 8\n2^2x = 2^3\n2x = 3\nx = 1.5\n\nlog8 8 = 1, since 8^1 = 8\n\nlog16 8 = x\n16^x = 8\n2^4x = 2^3\n4x = 3\nx = 3/4\n\nlog32 8 = x\n32^x = 8\n2^5x = 8\n5x = 8\nx = 8/5\n\nSo we have 3 + 1.5 + 1 + 3/4 + 8/5 = 7.85
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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
329438
log_5(X) + log_5(x-1)=log_5(6)\nlog_5(x(x-1)) = log_5(6)\nx(x-1) = 6\nx^2 - x - 6 = 0\n(x-3)(x+2) = 0\nx = 3 or x = -2\nYou cannot take the log of a negative number, so -2 cannot be a solution.\nAnswer: x=3\nFor the second part, find T(30) and T(75)\nT(30) = 70 + 100e^(-0.04(30))\n= 70 + 100(.3012)\n= 70 + 30.12\n= 100.12\n\nT(75) = 70 + 100e^(-.04(75))\n= 70 + 100(.0498)\n= 70 + 4.98\n= 74.98
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b^2=ac\nb^2x^2=ax*cx\n(bx)*(bx)=ax*cx\nflipping\n1/(bx)*1/bx=1/ax*1/cx\ntaking log\nlog1/bx+log1/bx=1/logax+1/logcx\n2/logbx=1/ax+1/cx
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log 2 x^2+1-log2^x\nlog 2 + log X^ + log 1 - (log 2^ + log X)\n=log 2 + A log X + log 1 - A log 2 - log X\n=log 2 + log 1- log X + A log (X - 2)\n=log (2 x 1) - log x + A log (x -2)\n=log 2/x + A log (x-2)\n=log 2/x + log (x-2)^\n= log (2/x X (x-2)^) = log 2/x(x-2)^
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2+2+2-(2/2)=5\n\n2^2+2-(2/2)=5\n\n2*2+2-(2/2)=5\n ___________________\n/ 22+2+(2/2)         =5\n\n ____________\n/(2*2)^2      +(2/2)=5\n\n (2+2+2)-(log2 to the base 2)\n\n [(2*2*2)+2]/2=5\n\n (2+2/2)!-(2/2)=5\n\n in all these put (log 2 to the base 2) instead of (2/2) then also it is 5\n\n (22-2)/(2*2)=5\n\n (22-2)/(2+2)=5\n\n (22-2)/(2^2)=5
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4^x - 4^(x-1) = 24\n4^x(1-4^(-1))= 24\n4^x * (3/4) = 24\n4^x = 32\n4^x = 4^(2.5)\nx=LOG(4,32)=2.5 Find (2x)^x = 5^(2.5) on calculator yourself or x=25*SQRT(2), SQRT-SQuare RooT.
815275
Using the quotient rule,\n\nlog(2x-1) - log(x-3)=1\nlog((2x-1)/(x-3)) = 1\n\nThen change to exponential form:\n\n10^1 = (2x-1)/(x-3)\n\nthen solve:\n\n10(x-3)=2x-1\n10x-30=2x-1\n8x=29\nx=29/8
259349
Solve by substitution.\nSolve for y^2 in the second equation by subtracting x^2 and 2x from both sides.\nx^2 + y^2 + 2x - x^2 - 2x = 19 - x^2 - 2x\ny^2 = 19 - x^2 - 2x  Now substitute this into the first equation in place of y^2\nx^2 + 2(19 - x^2 - 2x) = 33  Distribute the 2\nx^2 + 38 - 2x^2 - 4x = 33  Combine x^2 and -2x^2 and subtract 33 from both sides\n-x^2 - 4x + 5 = 0  Multiply both sides by negative one (I just do this because it is easier to factor when the x^2 is positive)\nx^2 + 4x - 5 = 0  Now factor\nWe are looking for factors of -5 that add up 4.  5 and -1 work because 5*(-1) = -5 and 5 - 1 = 4\nTherefore x^2 + 4x -5 = 0 becomes\n(x+5)(x-1) = 0  Set each part equal to 0\nx+5 = 0 or x-1 = 0\nTherefore,\nx = -5 or x = 1\nNow substitute each of these values into the y^2 equation from above.\ny^2 = 19 - x^2 - 2x\nFor x = -5\ny^2 = 19 - (-5)^2 - 2(-5)\ny^2 = 19 - 25 + 10\ny^2 = 4  Take the square root of each side to get\ny = -2 or 2\n\nFor x = 1\ny^2 = 19 - (1)^2 - 2(1)\ny^2 = 19 - 1 - 2\nY^2 = 16  Take the square root of each side to get\ny = -4 or 4\n\nThus, the solutions are\n(-5,-2), (-5,2), (1,-4), (1,4)\n\nIt is always good to check your answers, especially on a test.  To check your answers just plug each one into each equation to see if you get a true statement.
982509
Let log2 5 = x\n\nThen 2^x must be 5\n\nTake log of both sides but use log10 (common log, on calculator)\n\nx log 2 = log 5\n\nDivide both sides by log 2
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x = log(7)19\n\n7^x = 19\n\nx = (log19)/(log7)\nx = about 1.513
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2x/x^2 - 5x + 6 + 4/x - 2\n\nFirst we will simplify\n2x/x^2\n\nThe x on the top crosses out and the x^2 on the bottom becomes x.  We end up with 2/x.\n\n2/x - 5x + 6 + 4/x - 2\n\nNow we combine like terms.  All of the terms with just numbers will be added together.  Everything with something over x will be combined. \n\n(2/x + 4/x) - 5x + (6 - 2)\n\nWe have 6/x - 5x + 4\n\nNothing else can be combined so it is now in simplest form.