1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna [14]
3 years ago
6

What is the value of X?

SAT
2 answers:
soldi70 [24.7K]3 years ago
7 0

Answer:

x = 7

Explanation:

To solve for x in this equation, we're going to need to get the two exponents (3x - 5 and x + 1) equal to each other, but we can't do that unless our bases are the same.

For example, in A^{x} = B^{x + 1}, you cannot solve x = x + 1. In A^{x} = A^{x + 1}, you can solve x = x + 1.

Just by looking at the bases, 5 and 25, you can tell that it will be simple to make them match. 25 is just 5². The tricky part is going to be figuring out where to put the 2 into x + 1.

Let's look at another example. If you have 2^{2 * 2}, then you can simplify it to 2^{4}, which is 16. Or, you could do them one at a time, so (2^{2}) ^{2}. This way you'd have 4², which you'd be able to recognize as 16. Based on this example, we know that to make our bases the same, we need to change 25^{x + 1} to 5^{2(x + 1)}.

5^{3x-5} = 25^{x+1}   Change the right side to 5^{2(x + 1)}

5^{3x-5} = 5^{2(x+1)}   Simplify that exponent using distribution

5^{3x-5} = 5^{2x+2}  

Now that the bases match, you can get rid of them and just set the exponents equal to each other and solve for x.

3x - 5 = 2x + 2   Add 5 to both sides

3x = 2x + 7   Subtract 2x from both sides

x = 7

Now, check you work!

5^{3x-5} = 25^{x+1}   Plug in 7 for x

5^{3(7)-5} = 25^{(7)+1}   Simplify

5^{21-5} = 25^{8}   Simplify one more time

5^{16} = 25^{8}   Plug these into a calculator if you have one

152587890625 = 152587890625   So you know that x = 7 is correct.

nevsk [136]3 years ago
6 0

Answer:

<u>x = 7</u>

Explanation:

Because 25 is a perfect square of 5, we can turn

5^{3x - 5} = 25^{x + 1}

into

5^{3x - 5} = 5^{2x + 2}

Since the bases are now both equal, we can completely ignore them, as we are only trying to find x. This leaves us with:

3x - 5 = 2x + 2

All we have to do now is solve for x:

x - 5 = 2          <em>Subtract 2x from both sides.</em>

<u>x = 7</u>                <em>Add 5 to both sides.</em>

<em />

<em />

<em>Hope this helps! :)</em>

You might be interested in
A solute added to a solvent raises the boiling point of the solution because
katrin2010 [14]

Answer:

the solute particles raise the solvent's vapor pressure

Explanation:

3 0
3 years ago
Miedzy nami klasa 5 zad 1 str 249.
Ivanshal [37]

Answer:

this is hard idk

5 0
3 years ago
Today is your birthday! you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. To make this wi
marishachu [46]

You must earn an annual interest rate of 8.09%.

<h3><u>Compound interest</u></h3>

Given that you will deposit $75 a day each day for 17 years, and you deposit your first $75 today, to determine what annual interest rate you must earn in order for you to become a millionaire, you must perform the following calculation:

  • 40 - 23 = 17
  • 17 x 365 = 6205
  • 6205 x 75 = 465,375
  • 1 to 100 median = 57.9
  • 465,375 x 1.0809^(17 x 0.579) = X
  • 1,000,815 = X

Therefore, you must earn an annual interest rate of 8.09%.

Learn more about compound interest in brainly.com/question/25857212

8 0
2 years ago
Which of these methods is not safe for cooling food?
KiRa [710]

Answer:what are the methods

Explanation:

6 0
3 years ago
Read 2 more answers
Software that people commonly use in workplace is to make your life easier is called what
Alenkinab [10]
Productivity software is the response you are looking for
3 0
3 years ago
Other questions:
  • Which of these is the most likely effect of an increase in the cost of production?
    15·2 answers
  • 1. What's the cost of consumer credit?
    14·1 answer
  • Guys, I am taking the SHSAT and I am not confident I don't think I am smart enough to pass. I study like crazy but nothing stick
    14·1 answer
  • Arrange these decimals from least to greatest.
    13·2 answers
  • . Представьте, что в обычной российской семье школьника Ивана Серова шесть человек: мать, отец, сам Иван, его старшая сестра и б
    8·1 answer
  • How do the wavelength and frequency of the colors change as you move through the rainbow?
    14·1 answer
  • A polling company reported that 33% of 2286 surveyed adults said that they play football. Complete parts (a) through (d) below.
    6·1 answer
  • A study suggests that about 80\%80%80, percent of undergraduate students are working at a job. Researchers plan to do a follow-u
    13·1 answer
  • To say that an object is electrically polarized is to say that
    11·1 answer
  • There are many factors that contribute towards one's personal values and views toward nature. based on the information from this
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!