How Can You Solve the Equation 3^x + x = 4?

  • Thread starter Thread starter nineaxe
  • Start date Start date
  • Tags Tags
    Exponential
AI Thread Summary
To solve the equation 3^x + x = 4, isolating the exponential gives 3^x = 4 - x. Taking logarithms leads to the equation x log 3 = log(4 - x), but extracting x from the logarithm proves challenging. It is noted that an algebraic solution is not feasible. Observing the original equation suggests that an approximate value for x can be deduced intuitively. The discussion emphasizes the limitations of algebraic methods in solving this equation.
nineaxe
Messages
1
Reaction score
0

Homework Statement

3^x + x = 4

solve for x.

Homework Equations



I'm thinking of using the logarithm laws. log(a.b) = log a + logb log(a/b) = log a - log b

log(a^b) = bloga

The Attempt at a Solution


Well if I isolate the exponential
3^x = 4-x

take logs on both sides

xlog3 = log(4-x)

I can't seem to get the x out of the log.
 
Physics news on Phys.org
You won't be able to find a solution algebraically. However the value for x is quite obvious. Take a good look at the equation in its original form.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Solve the given equation that involves fractional indices
Replies
39
Views
3K
Rearranging Logarithms: Finding the Solution to log Equations
Replies
10
Views
3K
Solve for x: 2^3+2^3+2^3+2^3=2^x
Replies
3
Views
2K
Mastering Logarithms: Simplifying Complex Expressions with Multiple Logs
Replies
7
Views
2K
Finding the Value of axb on the Unit Circle | Round to the Nearest Thousandths
Replies
4
Views
2K
Can Logarithmic Properties Simplify This Equation?
Replies
12
Views
3K
Determine whether a logarithmic function is odd or even
Replies
11
Views
6K
Logarithm state the value of x for which the equation is defined
Replies
38
Views
6K
Solving for X: The Logarithmic Equations
Replies
3
Views
1K
Exponential and logarithmic Equation Problems
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top