# Mastering Exponential Equations: Get Urgent Help Now!

• bluegirlbalance
I should let you figure it out, but you seemed to be struggling.Okay, so the main thing to remember is that (a^n)^m=a^(nm). So if a=9, n=2x, and m=1, then (9^(2x))^1=9^(2x) and 9^(2x)=9^(x-1). Now, remember that 9 can be rewritten as 3^2, so we have (3^2)^(2x)=(3^2)^(x-1), which becomes 3^(4x)=3^(2x-2). Now we can set the exponents equal to each other to get 4x=2

#### bluegirlbalance

I totally need urgent help on these exponential equations. I am so confused write now. I know that the bases for each equation has to be the same and that is x is squared you have to factor or use the quadratic formula to find the solution. I also know that the general steps to solve these equations are to make the bases on each side of the equation the same. You have to set the exponents equal to each other. Lastly, you solve for x. I am still confused, I could do the examples in the lesson, but no these practice problems. Help!

1. 9^(2x)=27^(x-1)
2. 5^(n-1)=1/25
3. 25^x=5^(x^2-15)
4. (2^x)(4^(x+5))=4^(2x-1)
5. (sqrt 3)^(2x+4)=9^(x-2)

For the first equation, I think that x=-1. For the second equation, I think that n=1/2. For the other equations, I have no idea what to do.

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Firstly, it would help if you put brackets around the exponents. For example, is question 1. 92x=27x-1 or 92x=27x-1? I presume it is the former, but I disagree with your answer. Show your work; what base would you choose to take on each side? What equation does this yield?

cristo said:
Firstly, it would help if you put brackets around the exponents. For example, is question 1. 92x=27x-1 or 92x=27x-1? I presume it is the former, but I disagree with your answer. Show your work; what base would you choose to take on each side? What equation does this yield?
okay, since the base has to be the same of both sides, I say that 3 would be the base for this equation. I solved the problem and I got -1/5. Is this right?

bluegirlbalance said:
okay, since the base has to be the same of both sides, I say that 3 would be the base for this equation. I solved the problem and I got -1/5. Is this right?

Make your equation EXPLICIT at this point!

arildno said:
Make your equation EXPLICIT at this point!
1. 9^(2x)=27^(x-1)
Since the base has to be the same on both sides, I think that the base has to be changed to 3, making the equation read 3^(4)(2x)=3^(3)(x-1). You would set the exponents equal to each other: 8x=3x-1, which would give you x=-1/5. Is this the right answer for this problem, though?

No, it is not right, not your notation, and not your expression of 9, nor your contraction into an exponent equation.
We have:
$$9^{2x}=27^{(x-1)}, 9=3^{2},27=3^{3}\to(3^{2})^{2x}=(3^{3})^{x-1}\to3^{2*(2x)}=3^{3*(x-1)}$$
yielding the exponent equation:
$$2*(2x)=3*(x-1)$$

No. It is easy to verify that $9^{(2x)} \ne 3^{(4(2x)}$

arildno said:
No, it is not right, not your notation, and not your expression of 9, nor your contraction into an exponent equation.
We have:
$$9^{2x}=27^{(x-1)}, 9=3^{2},27=3^{3}\to(3^{2})^{2x}=(3^{3})^{x-1}\to3^{2*(2x)}=3^{3*(x-1)}$$
yielding the exponent equation:
$$2*(2x)=3*(x-1)$$
So I was right before, x= -1?

bluegirlbalance said:
So I was right before, x= -1?

Only if you believe -4=-6.

Do you understand what's going on here? We're saying that 9 can be represented by 3^2. Therefore, 9^x=(3^2)^x=3^(2x). Now the trick to solving these is to get them to the same base to get an 'exponent' equation.

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ZioX said:
Only if you believe -4=-6.

Do you understand what's going on here? We're saying that 9 can be represented by 3^2. Therefore, 9^x=(3^2)^x=3^(2x). Now the trick to solving these is to get them to the same base to get an 'exponent' equation.
maybe it would help if I showed what I did to get x=-1 and then you could tell me what I am doing wrong.
9^(2x)=27^(x-1)
=3^(2)(2x)=3^(3)(x-1)
=4x=3x-1
=x=-1
So where did you get -4=-6 from?

You are guessing (you original post) and being sloppy (your last post). What is [itex]3*(x-1)[/tex]?

bluegirlbalance said:
maybe it would help if I showed what I did to get x=-1 and then you could tell me what I am doing wrong.
9^(2x)=27^(x-1)
=3^(2)(2x)=3^(3)(x-1)
=4x=3x-1
=x=-1
So where did you get -4=-6 from?

You expand 3(x-1) as 3x-1. This is not correct. It should be 3(x-1)=3x-3

Do you understand how to multiply out a parenthesis?

bluegirlbalance said:
maybe it would help if I showed what I did to get x=-1 and then you could tell me what I am doing wrong.
9^(2x)=27^(x-1)
=3^(2)(2x)=3^(3)(x-1)
=4x=3x-1
=x=-1
So where did you get -4=-6 from?

Okay, you're doing quite a few things wrong. Please don't be so liberal with your equality symbols. Break it up. Go the long way. Don't do shortcuts, this is where you're getting messed up.

9^(2x)=27^(x-1) iff (3^2)^(2x)=(3^3)^(x-1) iff 3^(4x)=3^(3x-3) iff 4x=3x-3 iff x=-3.

The key thing to realize here is that (a^n)^m=a^(nm). (Where these formulas make sense...of course :| )

ZioX said:
Okay, you're doing quite a few things wrong. Please don't be so liberal with your equality symbols. Break it up. Go the long way. Don't do shortcuts, this is where you're getting messed up.

9^(2x)=27^(x-1) iff (3^2)^(2x)=(3^3)^(x-1) iff 3^(4x)=3^(3x-3) iff 4x=3x-3 iff x=-3.

The key thing to realize here is that (a^n)^m=a^(nm). (Where these formulas make sense...of course :| )
Thank you Zio X. you have been a real help and I get it know.

bluegirlbalance said:
Thank you Zio X. you have been a real help and I get it know.

Don't thank me, thank arildno. He already told you precisely what I did. Except I gave you a final answer...which I'm kind of regretting.

## What are exponential equations?

Exponential equations are equations in which the variable, or unknown quantity, appears in the exponent. These types of equations often involve exponential functions, which have a base raised to a power.

## Why is it important to master exponential equations?

Exponential equations are used in a wide range of fields, including finance, science, and engineering. Understanding and being able to solve these equations is crucial for solving complex problems and making accurate predictions.

## What are some strategies for mastering exponential equations?

Some strategies for mastering exponential equations include practicing with a variety of different examples, understanding the properties of exponential functions, and learning how to manipulate equations using logarithms.

## What are common mistakes to avoid when solving exponential equations?

Some common mistakes to avoid when solving exponential equations include forgetting to apply the exponent rules, misinterpreting negative exponents, and not checking for extraneous solutions.

## Where can I get urgent help with mastering exponential equations?

If you are struggling with mastering exponential equations, you can seek help from your teacher or a tutor. Additionally, there are many online resources and forums where you can ask for help and find step-by-step solutions to practice problems.