Properties of logarithms and logarithm properties of equalities

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Properties of logarithms and logarithm properties of equalities.Can you please show me how to solve this without having to use the quadratic method? I was already able to solve it using a quadratic expression, but I am wondering how to solve it a different way. The attachment is how I solved it by using the quadratic expression.2lnx — In(3x - 7) %3DIn(5x) - In (?+ 3) Inx2 21nx use power rule In(5x) n(5) n (x) use product rule In(3x 7) In(5) In(x) In (x+ 3) 21nx move portion to left side, change signs n(x)-n (x+3) 21nx In(3x 7) In(x) In(x +3) In (5) 21nx In(x) In (x) collect like terms In(x) In(3x-7) In(x 3)=In (5) In(x)In(x+3) - n (3x- 7) commutative property to reorder (x(x+3) In = In (5) quotient rule ??-7 x(? + 3) ?? -7 x2+3x 5 multiply each term in parenthesis by x ??-7 x2 3x 5(3x - 7) ?2 + 3x — 5(3?- 7) %3D 0 x23x 15x +35 0 multiply each side by 3x-7 move to left side, change sign multiply parenthesis by -5 x2 12x35 0 collect like terms (-12-4(1)(35 x 12)t solve quadratic equation 2(1)
12+2 12-2 = 7 2 2 Answer: x5,7 LC