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Math and Arithmetic

How do you solve for x in this problem v is the log base logv3 x plus logv3 parenthesis x-2 parenthesis equals 1?


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June 04, 2012 10:36PM

logbasev of (3x) + logbasev of 3(x-2)=1. Condense: logbasev of [3x(3)(x-2)]=1. Simplify: logbasev of [9(xsquared)-18x]=1. Convert to exponential form: v=9(xsquared)-18x. Set the equation equal to zero: 9(xsquared)-18x-v=0. Use the quadratic formula: x=[18±√(324+36v)]/18. Simplify: x=[18±√{36(9+v)}]/18. Simplify further: x=[18±6√(v+9)]/18. Factor out 6 everywhere: x=[3±√(v+9)]/3]. That is the final answer.