Question

Solve for x : (3*3^5x) / 9^2x = 1/27

Answer 1

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Answer 2

The required value of "x is equal to - 4".

Step-by-step explanation:

We have,

$\dfrac{(3\times 3^{5x}) }{9^{2x}} =\dfrac{1}{27}$

To find, the value of x = ?

∴ $\dfrac{(3\times 3^{5x}) }{9^{2x}} =\dfrac{1}{27}$

⇒ $\dfrac{(3^{5x+1}) }{(3^2)^{2x}} =\dfrac{1}{27}$

Using the exponential identity,

$a^{m} \times a^{n} =a^{m+n}$ and

$(a^{m})^n =a^{mn}$

⇒ $\dfrac{3^{5x+1}}{3^{4x}} =\dfrac{1}{27}$

⇒ $3^{5x+1-4x}=\dfrac{1}{3^3}$

Using the exponential identity,

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

⇒ $3^{x+1}=3^{-3}$

Comparing the power of 3 both sides, we get

⇒ x + 1 = - 3

⇒ x = - 3 - 1 = - 4

Thus, the required value of "x is equal to - 4".