Question

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

Answer 1

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.