How Do You Solve an Exponential Inequality with Different Bases?

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In summary, the conversation is about solving the inequality 2^x + 2^(4-x) > 17 and the attempt at a solution involves factoring for 2^(-x) and using the substitution u = 2x to simplify the expression. The final solution involves solving the inequality (u^2 - 17u +16)/u > 0 and finding the value of x.
  • #1
scientifico
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Homework Statement


2^x + 2^(4-x) > 17

2.The attempt at a solution
I factorized for 2^(-x) so I have 2^(-x) * (16 + 2^(2x)) > 17 but I don't know what to do after... could you help me ?

thanks
 
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  • #2


scientifico said:

Homework Statement


2^x + 2^(4-x) > 17

2.The attempt at a solution
I factorized for 2^(-x) so I have 2^(-x) * (16 + 2^(2x)) > 17 but I don't know what to do after... could you help me ?

thanks
Let u = 2x .
 
  • #3


how does it become ?
 
  • #4
That's what you're supposed to figure out and show us.
 
  • #5
Thanks I figured it out and solved correctly.

(u^2 - 17u +16)/u > 0
 
  • #6
scientifico said:
Thanks I figured it out and solved correctly.

(u^2 - 17u +16)/u > 0
What did you get when you solved for x ?
 

Related to How Do You Solve an Exponential Inequality with Different Bases?

What is an exponential equation?

An exponential equation is an equation in which the variable appears in the exponent. It is written in the form y = ab^x, where a and b are constants and x is the variable. These equations are commonly used to model situations where a quantity grows or decays at a constant rate.

How do you solve an exponential equation?

To solve an exponential equation, you can use logarithms. If the equation is in the form y = ab^x, you can take the logarithm of both sides to get log(y) = log(ab^x). Then, you can use the properties of logarithms to simplify the equation and solve for the variable.

What is the difference between an exponential equation and a linear equation?

An exponential equation has a variable in the exponent, while a linear equation has a variable that is raised to the first power. Exponential equations also have a constant ratio between each term, while linear equations have a constant difference between each term.

What are some real-life applications of exponential equations?

Exponential equations are used to model many real-life situations, such as population growth, compound interest, and radioactive decay. They are also used in fields like biology, economics, and finance to analyze and predict trends and patterns.

What are the properties of exponential equations?

Some properties of exponential equations include the power rule, product rule, quotient rule, and zero and negative exponent rules. These properties can be used to manipulate and solve exponential equations and make calculations easier.

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