S^4x = 27^x - 3 What is the value of x?

Mathematics

1 answer:

shtirl [24]3 years ago

8 0

Question :

$3^{4x}=27^{x-3}$ , What is the value of x?

Answer:

x = –9

Solution:

Given expression is $3^{4x}=27^{x-3}$ .

The bases of both sides of the equation must be same.

Convert Right side of the expression to base 3.

27 can be written as $3^3$ .

⇒ $3^{4x}=(3^{3})^{x-3}$

Apply exponent rule: $(a^m)^n=a^{mn}$

⇒ $3^{4x}=3^{3(x-3)}$

⇒ $3^{4x}=3^{3x-9}$

If the bases are same, then the powers are equal.

⇒ 4x = 3x – 9

Subtract 3x on both sides to equal the expression.

⇒ 4x –3x = –9

⇒ x = –9

Hence, the value of x is –9.

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