Question

find the value of 'n' in 6^n-2*3^n=3^n

Answer 1

Question:

find the value of 'n' in 6^n-2*3^n=3^n

Answer:

${6}^{n} - 2*3^n = {3}^{n} \\ = > \: {(2 \times 3)}^{n} - 2 \times {3}^{n} = {3}^{n} \\ = > \: {2}^{n} \times {3}^{n} - 2 \times {3}^{n} = {3}^{n} \\ = > \: {3}^{n} ( {2}^{n} - 2) = {3}^{n} \\ = > \: {2}^{n} - 2 = \frac{ {3}^{n} }{ {3}^{n} } \\ = > {2}^{n} - 2 = 1 \\ = > \: {2}^{n} = 3 \\ = > \: {2}^{n} = {2}^{1.5849} \\ as \: the \: bases \: are \: equal \: \\ comparing \: the \: powers \\ n = 1.5849$