Solve the exponential equation. x - 3 { 1 } = 2 6 3 (type a integer or a decimal. Round to the nearest thousandth as needed. Use a comma to seperate the answers as needed) 2/21/2014 | Keith from Gresham, OR | 3 Answers | 0 Votes Mark favorite Subscribe Comment
TO solve this equation we use logarithms as follows: (1/6)^{x-3}=(2/3) Take the natural logarithm (can also use log_{10}) of both sides and you get: ln(1/6)^{x-3}=ln(2/3) Because of the logarithmic property: ln(A)^{x}=xln(A) we get: (x-3)ln(1/6)=ln(2/3) If we divide both sides by ln(1/6) we get: x-3=[ln(2/3)]/[ln(1/6)] add 3 to both sides and we get: x=[ln(2/3)]/[ln(1/6)]+3 which has a decimal expansion as follows: 3.226 (rounded to thousandth as requested) Hope this helps :) 2/21/2014 | Charles A. Comment
(1/6)^(x-3) = 2/3 log((1/6)^(x-3)) = log(2/3) (x-3) log(1/6) = log(2/3) x log(1/6) - 3 log(1/6) = log(2/3) x log(1/6) = 3 log(1/6) + log(2/3) x = 3 + log(2/3)/log(1/6) x ≈ 3.22629438553092 ≈ 3.226 check: (1/6)^(3.22629438553092-3) =? 2/3 0.666666666666666 = 2/3 √ 2/21/2014 | Steve S. Comment
(1/6) ^( X -3) = 2/3 ( X -3 ) log ( 1/6) = log( 2/3) X -3 = log ( 2/3) / log ( 1/6) X = 3 + 0.2263 = 3. 2263 Test : ( 1/6) ^ ( 0.2263) = 0.66665996 It works. 2/21/2014 | Parviz F. Comment Comments The answer is tested, and it woks.i 2/21/2014 | Parviz F. Comment
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