Question

Find the value of x in the following.

$(\frac{3}{4})^{21} \times (\frac{3}{4})^{3} = ( \frac{3}{4}) ^{3x}$
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Answer 1

Answer:

x = 8

Step-by-step explanation:

Laws of exponents used:

$\star \: \: \sf{a^{m}\times a^{n}=a^{m+n}}$

★ When bases are equal, their powers can be equated.

Solution:

$\sf{\bigg(\dfrac{3}{4}\bigg)^{21}\times\bigg(\dfrac{3}{4}\bigg)^{3}=\bigg(\dfrac{3}{4}\bigg)^{3x}}$

Applying the first law of exponent from above,

$\implies \bigg(\dfrac{3}{4}\bigg)^{21+3}=\bigg(\dfrac{3}{4}\bigg)^{3x}$

$\implies \bigg(\dfrac{3}{4}\bigg)^{24}=\bigg(\dfrac{3}{4}\bigg)^{3x}$

Now, apply the second law of exponent from above;

→ 24 = 3x

⇒ 3x = 24

⇒ x = 24 ÷ 3

⇒ x = 8

∴ The value of x = 8