[tex] log10x \times 10(x + 3) = log{(10(x + 1))}^{2} \\ log(100 {x}^{2} + 300x) = log100 {(x + 1)}^{2} \\ 100 {x}^{2} + 300x = 100 {(x + 1)}^{2} \\ 100 {x}^{2} + 300x = 100( {x}^{2} + 2x + 1) \\ 100 {x}^{2} + 300x = 100 {x}^{2} + 200x + 100 \\ 300x = 200x + 100 \\ 300x - 200x = 100 \\ 100x = 100 \\ x = 1[/tex]
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[tex] log10x \times 10(x + 3) = log{(10(x + 1))}^{2} \\ log(100 {x}^{2} + 300x) = log100 {(x + 1)}^{2} \\ 100 {x}^{2} + 300x = 100 {(x + 1)}^{2} \\ 100 {x}^{2} + 300x = 100( {x}^{2} + 2x + 1) \\ 100 {x}^{2} + 300x = 100 {x}^{2} + 200x + 100 \\ 300x = 200x + 100 \\ 300x - 200x = 100 \\ 100x = 100 \\ x = 1[/tex]