Question

please answer the question chapter is exponents and power....​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\rm \underline{Solution-}$

We have,

$\rm \bigg( \frac{1}{ {3}^{2} } \bigg) ^{x} = \frac{1}{ {3}^{6} }$

Calculate 3 to the power of 2 and get 9.

$\rm⟹ \bigg( \frac{1}{9} \bigg) ^{x} = \frac{1}{ {3}^{6} }$

Calculate 3 to the power 6 and get 729.

$\rm⟹ \bigg( \frac{1}{9} \bigg) ^{x} = \frac{1}{729}$

Take the logarithm of both the equation.

$\rm⟹ log \bigg( \bigg( \frac{1}{9} \bigg ) ^{x} \bigg) = log \bigg( \frac{1}{729} \bigg)$

The logarithm of a number raised to a power is the power time to logarithm of the number.

$\rm⟹ x \: log \bigg( \frac{1}{9} \bigg) = log \bigg( \frac{1}{729} \bigg)$

Divide both by log ( ⅑).

$\rm⟹ x = \frac{log \bigg( \frac{1}{729} \bigg)}{log \bigg( \frac{1}{9} \bigg) }$

By the change of base formula [log(a)/log(b) = log_b (a).

$\rm⟹ x = log \: \frac{1}{9} \bigg( \frac{1}{729} \bigg)$

$\rm⟹ x = \boxed{ 3 }\:Ans.$

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