Question

find the value of x, if 3^4*3^5=(3^3)^x

Answer 1

Answer :

Given,

3⁴ × 3⁵ = (3³)ˣ

⇒ 3⁴⁺⁵ = (3³)ˣ

⇒ 3⁹ = (3³)ˣ

⇒ (3³)³ = (3³)ˣ

Comparing both sides, we get x = 3

∴ The required value of x is 3

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Answer 2

Answer:

The value of x is 3

Step-by-step explanation:

Given $3^{4}\times 3^{5}=(3^{3})^{x}$

Using the rule of indices,

• bases are same, powers can be added. $a^{x}\times a^{y}=a^{x+y}$
• power raised to a power, then powers are multiplied together.$(a^{x})^{y}=(a)^{xy}$

the given equation can be written as

$3^{4}\times 3^{5}=(3^{3})^{x}\implies 3^{4+5}=3^{3x}$

$\implies 3^{9}=3^{3x}$

When bases are equal, powers are also equal, $a^{x}= a^{y} \implies x=y$

Therefore, equating the powers, $3x=9$

$\implies x=\frac{9}{3} =3$

Hence, the value of x is 3.