Question
:
[tex]3^{4x}=27^{x-3}[/tex], What is the value of x?
Answer:
x = –9
Solution:
Given expression is [tex]3^{4x}=27^{x-3}[/tex].
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 [tex]3^3[/tex].
⇒ [tex]3^{4x}=(3^{3})^{x-3}[/tex]
Apply exponent rule: [tex](a^m)^n=a^{mn}[/tex]
⇒ [tex]3^{4x}=3^{3(x-3)}[/tex]
⇒ [tex]3^{4x}=3^{3x-9}[/tex]
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.
