The solution is x = -5
Step-by-step explanation:
Given equation is:
[tex]3^{(x-1)} = 9^{(x+2)}[/tex]
In order to solve the eponnetial equations, we have to equate the bases of both sides so that the exponents can be put equal
So,
Replacing 9 with 3^2
[tex]3^{(x-1)} = (3^2)^{(x+2)}[/tex]
When there are exponents on exponents, both are multiplied so,
[tex]3^{(x-1)} = 3^{(2x+4)}[/tex]
As the bases on both sides are same, the exponents can be put equal
So,
[tex]x-1 = 2x+4[/tex]
Adding 1 on both sides
[tex]x-1+1 = 2x+4+1\\x = 2x+5[/tex]
Subtracting 2x from both sides
[tex]x-2x = 2x-2x+5\\-x = 5\\x = -5[/tex]
Hence,
The solution is x = -5
Keywords: Exponents, Equations
Learn more about exponential equations at:
- brainly.com/question/1993757
- brainly.com/question/2115122
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