Logarithmic Equations and Substitution

For a base a>0, a 1, when both a2x and ax occur, let u=ax, so u>0. Solve the polynomial in u, reject non-positive values and then recover x. For a logarithmic equation, record the positive-argument restrictions first. Combine logarithms with matching bases, solve the resulting equation and test every candidate in the original domain. Squaring or clearing factors can introduce inadmissible roots. A graphical solution is an intersection of the two sides or a zero of their difference. Choose a window that respects the domain and check all visible branches; a graph supports a numerical answer but does not replace exact algebra when an exact value is requested.