3^x-5 =27...please help solve?
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First, there is a difference between\n1) 3^x-5=27 and\n2) 3^(x-5)=27    1) means raise 3 to the x power, then\n\nsubtract 5 , 2) means subtract 5 from x and raise 3 to that power.\nCheck your original and be sure. In math, we're extremely\nand totally precise. It's part of the whole academic discipline. \n  About you log key : Calculators are different so you will have to experiment a little. Key in 10 then hit log. You\nmust get 1. For now ignore confusing issues with the use\nof ln, you don't need to know that. To make sure, key in\n100 and hit log. You must get 2.\n  No for anti log or inverse log experiment some more and/or get help. Key in 1 and punch your inverse log\nsequence or key. The answer must be 10. Again do it for 2.\nThe answer must be 100. When you have mastered that then\nproceed to the problem.\n Assume your problem is 1). Then add 5 to both sides of the equation giving you 3^x=32. Now solve\n x(log(3))=log(32)\nx=log(32)/log(3) \nTake the log of 32 giving 1.505  .\nTake the log of 3 giving .477  so\nx=1.505/.477 = 3.155\n\n If the problem was actually 2) then we have\n(x-5)(log(3))=log(27)\n(x-5)=log(27)/log(3) = 1.43/.477 = 3.00\nx=8
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the different stages go like this:\nx-3/5=x-5\nx-3=5x-25\n-3=4x-25\n0=4x-22\n22=4x\nx=5.5
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start pulling out common factors\n\n2 (x^3 + 27)\n\n2(x^3 + 3^3)
271727
x^2 + 12x + 27 = 0\n(x+9)(x+3)=0\nso...\nx+9=0\n  x=-9\nand\nx+3=0\n  x=-3
54462
(3x+5)/wz \n(3*4+5)/(-1*5)\n(15+5) / (-1*5) \n20/-5 = -4
416859
There is a rule of exponents that says (x^a)(x^b) = x(a+b).  Use this in reverse:\n\n(3^2x) - 3^(2x - 1) = 18\n(3^2x) - [3^(2x)*3^(- 1)] = 18\n(3^2x) - (3^(2x))/3 = 18\n3(3^2x) - (3^2x) = 54\n2(3^2x) = 54\n(3^2x) = 27\nlog(3^2x) = log27\n2xlog3 = log27\nx = log27/2log3\n= 1.5
877752
Forty.\nCross multiply/divide  \n5/8=25/x\nmultiply both sides by x and both sides by 8\nyou get\n5x=25 times 8\n\nx = (25x8)/5  or x=25/5 x 8 or x = 5 x 8
901403
Do you mean\n\n3^(x+5) = 9^x → 3^(x+5) = 3^(2x)  → x = 5\n\nOr\n\n3^x+5 = 9^x\nie 3^(2x) = 3^x + 5\nSo [3^(x)]² - 3^x - 5 = 0\nLet v = 3^x\nThus v² - v - 5 = 0\nSo v = ½{1 ± √[(-1)² - 4.(1)*(-5)]}\n= ½ (1 ± √21)\nSince v = 3^x and we seek real solutions\nv = ½ (1 + √21)\nSo 3^x = ½ (1 + √21)\nx = log [½ (1 + √21)] / log3\n≈ 0.9344\n\nCheck\nLHS = 3^x + 5 ≈ 3^(0.9344) + 5 ≈ 7.791\nRHS = 9^x ≈ 9^(0.9344) ≈ 7.792 (Differences are from truncation errors)
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You need to give some directions.  What is the problem asking you to do?\nNote: The person below is incorrect.  (4+3x)^5 does NOT equal\n4^5 + (3x)^5
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This is works like n-2^(n-2) \n1-1 = 1-2^(2-2) = 1-2^0 = 1-1\n3-2 = 3-2^(3-2) = 3-2^1 = 3-2\n5-8 = 5-2^(5-2) = 5-2^3 = 5-8\n7-x = 7-2^(7-2) = 7-2^5 = 7-32 \nThus x is 32.
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bring the a's to one side... u then get 9a = 27 ... divide and answer is a = 3
969851
Basically there're 2 approaches to this problem:\n\n1. Factoring -- easy but NOT applicable to ALL problems.\nAfter factoring, it becomes:\n(5x+1)(3x+5)=0 (cuz 15=5*3, 5=1*5, and 28=5*5+3*1)\ntherefore either 5x+1=0 or 3x+5=0\nthen the two real roots are:\nx=-1/5, -5/3\n\n2. Quadratic formula -- general & reliable but more work. \nAssuming u know the formula (if not look it up in ur math book), just go head and plug in all corresponding coefficients of the original equation (here a=15, b=28, c=5), yields:\nx=(-28+/-square root of (28^2-4*15*5))/(2*15)=-1/5, -5/3\nwhich gives u exactly the same answers as method 1.\n\nHope these make sense to u.. GoOd Luck!..^^
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You do not need to use logs.\n27 can be written in base 3\n27 = 3^3\nTherefore,\n27^4 = (3^3)^4\nMultiply the exponents to get\n27^4 = 3^12\nThus, your equation is not\n3^x = 3^12\nWhenever the bases are the same, then the exponents are equal.\nTherefore,\nx = 12
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1, 3, 9, 27.\n\nThese are the powers of 3 if you noticed.\n\n2 = 3-1\n4 = 3+1\n5 = 9 -3-1\netc.
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Working with equation 2:\n\n5^2[2^(x-4) +5^(y-2)]=13*25\n5^2*2^(x-4) + 5^y = 325\n\nAdd this to 1st equation, yielding\n\n5^2*2^(x-4) + 2^(x+1) = 456\n2^(x-4)[5^2 + 2^5] = 456\n2^(x-4) = 456/(25+32)\n2^(x-4) = 8\nx-4 = 3\nx = 7\n\nUse 1st equation:\n\n2^8 - 5^y = 131\n5^y = 256 - 131 = 125\ny = 3
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A number, to the power of 3. (i.e. 27=3-cubed, or 3X3X3)
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First, you can easily run this through Google Calculator and get the answer of 52 (see link below)... or I can show you the steps:\n\n(30-4(5-2))+5(27-25)sqrt(9)+sqrt(16)\n= (30-4(3)) + 5(2)(3) + 4\n= (30-12) + 5(6) + 4\n= 18 + 30 + 4\n= 52\n\nNote: This *is* the correct answer.  What the other people are forgetting is the order of precedence.  When there are no parentheses, multiplication takes precendence over addition and subtraction.\n\nThe equation really simplifies down to 18 + 10 x 3 + 4. \nOne answer incorrectly added 18+10 before multiplying by 4 then adding 3. The other answer incorrectly added 4+3 before multiplying by 10.\n\nYou must do the multiplication first (10 x 3) and then the result is 18 + 30 + 4.\n\nSo the answer is definitely 52.  If you don't believe me check Google.