Question

Solve log base 7(x³+27)-log base 7(x+3)=2​

Answer 1

Explanation:

$\sf {log}_{7}{{x}^{3}+27} - log_{7}{x+3} = 2 \\ \\ \sf \longrightarrow {log}_{7}{\frac{{x}^{3}+27}{x+3}} = 2 \\ \\ \sf \longrightarrow {log}_{7}{\frac{{x}^{3} + {3}^{3}}{x+3}} = 2 \\ \\ \sf \longrightarrow {log}_{7}{\frac{(x+3)({x}^{2}-3x+{3}^{2})}{x+3}} = 2 \\ \\ \sf \longrightarrow {log}_{7}{{x}^{2}-3x+9} = 2 \\ \\ \sf \longrightarrow {x}^{2} - 3x + 9 = {7}^{2} \\ \\ \sf \longrightarrow {x}^{2} - 3x + 9 = 49 \\ \\ \sf \longrightarrow {x}^{2} - 3x - 40 = 0 \\ \\ \sf \longrightarrow {x}^{2} - 8x + 5x - 40 \\ \\ \sf \longrightarrow (x-8)(x+5) = 0 \\ \\ \sf \longrightarrow x = 8 , -5 \\ \\ \sf -5\:is\:not\: accepted \\ \\ \sf so\:the\: answer \: is \: x = 8$