Question

Simplify:
${3}^{3x} + 9 = 10 \times {3}^{x}$
What is the value of x
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Answer 1

Solution :

The given equation is

3³ˣ + 9 = 10 × 3ˣ

⇒ (3ˣ)³ + 9 = 10 × 3ˣ

⇒ a³ + 9 = 10a [ let a = 3ˣ ]

⇒ a³ - 10a + 9 = 0

⇒ a³ - a - 9a + 9 = 0

⇒ a (a² - 1) - 9 (a - 1) = 0

⇒ a (a + 1) (a - 1) - 9 (a - 1) = 0

⇒ (a - 1) {a (a + 1) - 9} = 0

⇒ (a - 1) (a² + a - 9) = 0

∴ Either a - 1 = 0 or, a² + a - 9 = 0

We take a = 1; we are not going to take the irrational value of a in order to find the value of x

Now, a = 1

⇒ 3ˣ = 3⁰ [ since a = 3ˣ ]

Comparing among coefficients, we get x = 0, which is the required solution.