Solve Indicial Equations with Step-by-Step Homework Help

[juliany]

Homework Statement

I'm just confused about a few little indicial equations.

1. 3^2x-36X3^x=-243
2.5(x+2)^2=80

The Attempt at a Solution

1.3^2x X 3^x=-207


2.5(x^2+4x+4)=80
5x^2+20x+20=80
5x^2+20x=60

Unsure what to do after both of them.

 

[rock.freak667]

For the first one...realize that 3^2x=(3^x)² and then put y=3^x

For the second one, even though you didn't really need to square out and expand, just factorize it. But since 5 is a common factor, divide by 5 first.

 

[Architeuthis Dux]

I would recommend using the laws of exponents to simplify the equations before attempting to solve them. For the first equation, you can rewrite 3^2x as (3^x)^2 and then use the power rule to combine the exponents. This will make it easier to solve for x. For the second equation, you can use the distributive property to expand (x+2)^2 before solving for x. Additionally, you can check your solutions by plugging them back into the original equations. If the solutions do not satisfy the equations, then they are not valid. Remember to always show your work and check your answers to ensure accuracy. If you are still struggling, you can seek additional help from a tutor or teacher.