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Marta_Voda [28]
3 years ago
10

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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