Solve Exponential Equation: 5^(sqrt(x)) + (1/5)^(sqrt(x)) = 25

  • Thread starter Thread starter scientifico
  • Start date Start date
  • Tags Tags
    Exponential
Click For Summary
SUMMARY

The discussion focuses on solving the exponential equation 5^(sqrt(x)) + 5 * 5^(-sqrt(x)) = 25 + 1/5. A key transformation involves substituting u = 5^(sqrt(x)), which simplifies the equation to u + 5/u = 25 + 1/5. This substitution allows for easier manipulation and solving of the equation, leading to a clearer path to the solution.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with algebraic manipulation techniques
  • Knowledge of substitution methods in solving equations
  • Basic skills in handling rational expressions
NEXT STEPS
  • Study the properties of exponential functions and their graphs
  • Learn about substitution methods in algebraic equations
  • Explore rational expressions and their simplification techniques
  • Practice solving similar exponential equations for proficiency
USEFUL FOR

Students studying algebra, particularly those tackling exponential equations, as well as educators looking for effective teaching methods in algebraic problem-solving.

scientifico
Messages
181
Reaction score
0

Homework Statement


5^( \sqrt(x) ) + 5 * 5^(- \sqrt(x) ) = 25 + 1/5

2. The attempt at a solution

I have thought to transform 5^ (-\sqrt(x) ) in (1/5)^(\sqrt(x) ) but I don't know how to solve then... could you help me ?

thank you
 
Physics news on Phys.org
scientifico said:

Homework Statement


5^( \sqrt(x) ) + 5 * 5^(- \sqrt(x) ) = 25 + 1/5

2. The attempt at a solution

I have thought to transform 5^ (-\sqrt(x) ) in (1/5)^(\sqrt(x) ) but I don't know how to solve then... could you help me ?

thank you

That's a good idea. So if u=5^(sqrt(x)) then 5^(-sqrt(x)) equals 1/u. Solve for u first.
 

Similar threads

Rationalize the denominator: ##\sqrt{\dfrac{1}{2x^3y^5}}##
  • · Replies 6 ·
Replies
6
Views
3K
Find the value of ##\sqrt[5]{0.00000165}##
  • · Replies 4 ·
Replies
4
Views
2K
Problems in manipulating these 4 radical equations
  • · Replies 8 ·
Replies
8
Views
2K
Quadratic inequalities with absolute values
  • · Replies 7 ·
Replies
7
Views
2K
Solve ##\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}}=4\dfrac{1}{4} \cdots##
  • · Replies 10 ·
Replies
10
Views
3K
Is there a rule that states that I should not divide in this scenario?
  • · Replies 10 ·
Replies
10
Views
2K
Solve the equation : ##x^4+12x^3+2x^2+25=0##
  • · Replies 24 ·
Replies
24
Views
4K
How Can You Solve This Modulus Equation with Square Roots and Absolute Values?
  • · Replies 1 ·
Replies
1
Views
2K
How to prove this without using Cardano's formula?
  • · Replies 8 ·
Replies
8
Views
3K
Comparing Solutions of Quadratic Equations: Real vs Imaginary Roots
  • · Replies 3 ·
Replies
3
Views
2K