Question

${3}^{x - 1} = \frac{1}{27}$
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Answer 1

$\huge\mathfrak\purple{Heya\:Mate}$❤

${3}^{x - 1} = \frac{1}{27} \\ \\ {3}^{x - 1} = \frac{1}{ {3}^{3} } \\ \\ {3}^{x - 1} = {3}^{ - 3} \\ \\ x - 1 = - 3 \\ \\ x = - 3 + 1 \\ \\ x = -2$

Hope it helps uhh✌✌✌

Answer 2

${3}^{x - 1} = \frac{1}{27}$

27 is Cube of 3

3³=27

Means

${3}^{x - 1} = \frac{1}{ {3}^{3} }$

1/a^x=a^-x

$3 {}^{x - 1} = {3}^{ - 3}$

If a^x=a^y

X=Y

$x - 1 = - 3 \\ \\ x = - 3 + 1 \\ \\ x = - 2$

x=-2

Check

$3 {}^{x - 1} \\ \\ {3}^{ - 2 - 1} \\ \\ {3}^{ - 3} \\ \\ \frac{1}{ {3}^{ 3} } \\ \\ \frac{1}{27}$

Hence LHS=RHS

X=-2