How to Solve the Equation log(4x) = 1 + log(2, 2x)?

  • Thread starter Thread starter Wayne123
  • Start date Start date
  • Tags Tags
    Log
Click For Summary
SUMMARY

The equation log(4x) = 1 + log(2, 2x) can be solved by applying logarithmic properties. First, rewrite log(4x) as log(4) + log(x), which simplifies to 2 + log(x) since log(4) = 2. The right side can be simplified using the change of base formula, yielding log(2) + log(2x) = log(2) + log(2) + log(x) = 2 + log(x). Setting both sides equal leads to the conclusion that the equation holds for all x > 0.

PREREQUISITES
  • Understanding of logarithmic properties
  • Familiarity with the change of base formula
  • Basic algebra skills
  • Knowledge of solving equations
NEXT STEPS
  • Study logarithmic identities and their applications
  • Learn about the change of base formula in depth
  • Practice solving exponential equations
  • Explore advanced topics in precalculus, such as functions and their transformations
USEFUL FOR

Students studying precalculus, educators teaching logarithmic functions, and anyone seeking to enhance their algebraic problem-solving skills.

Wayne123
Messages
3
Reaction score
0
Solve the equation log4x=1+log22x, x>0
 
Physics news on Phys.org
The form you started with had three sections, including relevant equations and your efforts at a solution. What are some relevant equations, and what have you tried to solve this equation?

BTW, this should have gone into the Precalculus section, not the Calculus & Beyond section.
 

Similar threads

Differentiation of Log(cos(X)/x^2)^2
  • · Replies 6 ·
Replies
6
Views
2K
Is log(x) well-defined on [-1,1]?
  • · Replies 15 ·
Replies
15
Views
2K
Solving for z in the Equation tan z = 1 + 2i
  • · Replies 3 ·
Replies
3
Views
2K
Solving Homework Equations for x & y with 2x + 3y + 1 = 0
  • · Replies 3 ·
Replies
3
Views
2K
Verify the convergence or divergence of a power series
  • · Replies 17 ·
Replies
17
Views
2K
Power series: Why is this power series equal to log(2)?
  • · Replies 2 ·
Replies
2
Views
1K
Finding domain for when composite function is continuous
  • · Replies 3 ·
Replies
3
Views
1K
Solve the simultaneous equations
  • · Replies 11 ·
Replies
11
Views
1K
Finding Values of Complex Equation
  • · Replies 1 ·
Replies
1
Views
1K
When to Use Ln vs Log in Calculating Derivatives?
  • · Replies 7 ·
Replies
7
Views
4K