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It isn't clear what you want to solve for. If you want to find the matrix, there is not a unique solution - there are infinitely many matrices with the same determinant.
log(f) + log(0.1) = 6 So log(f*0.1) = 6 so f*0.1 = 106 so f = 107
A single math equation does not have a determinant. A system of equations (3x3 , 4x4, etc.) will have a determinant. You can find a determinant of a system by converting the system into a corresponding matrix and finding its determinant.
Matrix inverses and determinants, square and nonsingular, the equations AX = I and XA = I have the same solution, X. This solution is called the inverse of A.
You can't solve this since it isn't an equation.There is also an ambiguity (it's hard to write math on a typewriter keyboard) - are we talking about log(x3) or maybe logx(3)?Restate the question: Simplify log(x3)Answer: 3log(x)You could explain this by saying: log(x3) = log[(x)(x)(x)] = logx + logx + logx = 3logx. The general rule is log(xn) = nlogx.