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
IRISSAK [1]
3 years ago
8

5^(2x-1)+5^(x+1)=250 how do you solve? thank you

Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

<em>x = 2</em>

Step-by-step explanation:

<u>Exponential Equations</u>

Solve:

5^{2x-1}+5^{x+1}=250

Separate each exponential:

5^{2x}5^{-1}+5^{x}5^{1}=250

Operating:

\displaystyle \frac{5^{2x}}{5}+5^{x}5=250

Multiplying by 5:

5^{2x}+25\cdot5^x=1250

Rearranging:

5^{2x}+25\cdot5^x-1250=0

Recall that:

5^{2x}=(5^{x})^2

(5^{x})^2+25\cdot5^x-1250=0

Calling

y=5^{x}:

y^2+25y-1250=0

Factoring:

(y-25)(y+50)=0

There are two possible solutions:

y=25

y=-50

Since

y=5^{x}

y cannot be negative, thus:

5^{x}=25=5^2

The solution is:

x = 2

You might be interested in
Find parametric equations for the line parallel to r=(6,-8) and passing through P(9,-1)
fgiga [73]

Answer:

x=6t+9 y=-8-1

Step-by-step explanation:

8 0
3 years ago
Help me please how do I get the answer to 7.44 divided by 6 equals
dalvyx [7]
<span>7.44 divided by 6 = 1.24
hopes this helps.</span>
5 0
2 years ago
Read 2 more answers
Convert 2% to a decimal
nalin [4]

Answer: 0.02

Step-by-step explanation: Divide 2 by 100

5 0
3 years ago
Read 2 more answers
What is the area of a rectangle that has a length of 1/4 inch and a width of 1/8 inch?
Lubov Fominskaja [6]

Answer:

1/4 * 1/8 = 1/32 inch

Step-by-step explanation:

1/4 * 1/8 = 1/32inch

8 0
2 years ago
Which of the b-values satisfy the following inequality?5 &lt; b - 3Choose all the answers that apply: A.) b = 8B.) b = 9C.) b =
dusya [7]
[tex]\begin{gathered} \text{The inequality is,} \\ 5
4 0
1 year ago
Other questions:
  • S+(s+.89)=92.99 please help
    7·1 answer
  • every evening jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she
    5·1 answer
  • Find the vertex of the given quadratic function.
    11·1 answer
  • 6 times the sum of a number and 5 is 16
    8·1 answer
  • Can anyone help please right answer only
    8·1 answer
  • What is the result when 12x2-7y2 is added by -10x2+y2?
    14·1 answer
  • Es equivalente?<br><br>2 10<br>- y -<br>3 15​
    6·1 answer
  • What can be multiplied to get 40 but also added to get 29​
    5·1 answer
  • Write as a simple fraction for x+3/x-3 - x-2/x+2​
    5·2 answers
  • Which of the following is a solution to the equation y=-1/4x +8 O (10,8) 0 (48) O (49) O (-8.-10)​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!