__Example 1__Solve the following equation:

(a) ${\mathrm{log}}_{3}2+{\mathrm{log}}_{3}(x+5)={\mathrm{log}}_{3}(3x-1)$

(b) ${\mathrm{log}}_{2}8x-3={\mathrm{log}}_{2}(2x-1)$

(c) $3{\mathrm{log}}_{x}2+2{\mathrm{log}}_{x}4-{\mathrm{log}}_{x}256=-1$

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