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Homework Statement
For what x does [tex]x + 3^x < 4[/tex]
Homework Equations
The Attempt at a Solution
The thing is = 4 when x is 1. So I want x < 1.
But is there a way to do this algebraically? Like with log or something?
The purpose of this inequality is to determine the values of x that satisfy the given expression. In other words, we are trying to find the values of x that make the inequality true.
The exponent, x, represents the power to which the base, 3, is raised. In this case, we are interested in finding values of x that make the expression less than 4 when added to x.
To solve this inequality, you can use algebraic techniques such as isolating the variable and factoring. You can also use graphical methods to visually determine the values of x that satisfy the inequality.
Yes, there are restrictions on the values of x. Since we are dealing with a logarithmic function, x must be a positive real number. Additionally, x cannot be equal to 1 since 3^1 = 3, which would make the expression equal to 4, not less than 4.
Inequalities like this one are commonly used in mathematics and science to model real-life situations such as population growth, compound interest, and radioactive decay. Solving these types of inequalities helps us understand and make predictions about these phenomena.