You cannot solve log x- 2 unless (i) log x - 2 is equal to some number or (ii) x is equal to some number.
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log(x) + log(2) = log(2)Subtract log(2) from each side:log(x) = 0x = 100 = 1
3^(-2x + 2) = 81? log(3^(-2x + 2)) = log(81) (-2x+2)log(3) = log(81) -2x = log(81)/log(3) - 2 x = (-1/2)(log(81)/log(3)) + 1
9x = 27 log(9) + log(x) = log(27) log(x) = log(27) - log(9) log(x) = log(27/9) 10log(x) = 10log(27/9) x = 27/9 x = 3 This strikes us as the method by which the federal government might solve the given equation ... after appointing commissions to study the environmental impact and recommend a method of solution, of course.
e^2-x = 10^x-2 let take the natural log of both sides we have 2-x=ln ( 10^(x-2) 2-x=x-2(ln 10) 4-2x=ln10 -2x=ln10-4 x= -1/2[(ln10)+4)]
2 log(x) = log(8)log(x2) = log(8)x2 = 8x = sqrt(8) = 2.82843 (rounded)Note that only the positive square root of 8 can serve as a solution to thegiven equation, since there's no such thing as the log of a negative number.