Question

Find x, if (1/3)^-4 x (1/3)^-8 = (1/3)^-2x

Answer 1

`{ \overline{ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}`

`\large \underline \mathbb{PROBLEM : }`

`\qquad\quad\tt{Solve \: for \: x} : \\ \\\qquad\quad \sf \: \bigg( (1)/(3)\bigg)^( - 4) * \bigg( (1)/(3)\bigg)^( - 8) = \bigg( (1)/(3)\bigg)^( - 2x) \\ \\ \\`

`{ \overline{ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}`

`\large \underline \mathbb{ANSWER : }`

`\qquad \qquad \quad\qquad \huge \tt{x = 6 }\\ \\`

`{ \overline{ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}`

`\large \underline \mathbb{SOLUTION : }`

Given :-

`\qquad\quad\large\sf \: \bigg( (1)/(3)\bigg)^( - 4) * \bigg( (1)/(3)\bigg)^( - 8) = \bigg( (1)/(3)\bigg)^( - 2x) \\ \\`

We know :-

`\qquad \qquad\large\boxed{ \sf{ \: {a}^(x) * {a}^(y) = {a}^(x + y) \: }} \\ \\`

We get :-

`\large\sf \Longrightarrow \qquad \bigg( (1)/(3)\bigg)^( - 4 + ( - 8)) = \bigg( (1)/(3)\bigg)^( - 2x) \\ \\`

`\large\sf \Longrightarrow \qquad \bigg( (1)/(3)\bigg)^( - 4 - 8) = \bigg( (1)/(3)\bigg)^( - 2x) \\ \\`

`\large\sf \Longrightarrow \qquad \bigg( (1)/(3)\bigg)^( - 12) = \bigg( (1)/(3)\bigg)^( - 2x) \\ \\`

We know :-

`\large \qquad \qquad\boxed{ \sf{ \: {a}^(x) = {a}^(y) \: \sf \: \implies \: x = y \: }} \\ \\`

So,

`\large\sf\Longrightarrow \quad - 12 = - 2x \\ \\`

`\large\sf\Longrightarrow \quad \underline{\sf {\red{x = 6}}} \: \sf{ --- \: Final \: Answer} \\ \\`

`\underline{\rule{190pt}{8pt}} \\`

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`\large \mathfrak{TheFletchhhh \: \: X'D}`