Question

plz provide detailed answer of this question , if possible plz don't text the answer send pic​

Answer 1

Answer:

$\huge{\boxed{\pink{x = 2}}}$

Step-by-step explanation:

$\bold{\underline{\blue{Given}}}\longrightarrow \\ log_{3}( {3}^{x} - 6 ) = x - 1$

$\bold{\underline{\green{Concept \: used}}}\longrightarrow \\if \\ log_{m}(x) = n \: = > x = {m}^{n}$

${a}^{m - n} = {a}^{m} \: \: {a}^{ - n}$

$\bold{\underline{\red{Solution}}}\longrightarrow \\ log_{3}( {3}^{x} - 6 ) = x - 1 \\ = > {3}^{x} - 6 = {3}^{x - 1} \\ = > {3}^{x} - {3}^{x - 1} - 6 = 0 \\ = > {3}^{x} - {3}^{x} \: \: {3}^{ - 1} = 6 \\ = > {3}^{x} (1 - \dfrac{1}{3} ) = 6 \\ = > {3}^{x} ( \dfrac{3 - 1}{3} ) = 6 \\ = > {3}^{x} ( \dfrac{2}{3} ) = 6 \\ = > {3}^{x} = \dfrac{6 \times 3}{2} \\ = > {3}^{x} = \dfrac{18}{2} \\ = > {3}^{x} = 9 \\ = > {3}^{x} = { {3}^{2} } \\ comparing \: exponent \: we \: get \\ = > x = 2$