Logarithmic Inequalities: Solving e^(2-3x)>4

  • Thread starter EL ALEM
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    Logarithmic
In summary, to solve the inequality e^(2-3x)>4, we take the natural log of both sides to get 2-3x>ln(4). Then, we can solve for x by subtracting 2 and dividing by -3, giving us the final solution of x<(2-ln(4))/3.
  • #1
EL ALEM
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Homework Statement


Solve the inequality:
e^(2-3x)>4


Homework Equations


none



The Attempt at a Solution


would i start of like this?
e^(2-3x)>4
ln(2-3x)>ln4

if so how do i continue?
 
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  • #2
Forget that, I figured it out. I started it off kinda wrong.
 
  • #3
yes el alem u r rite ...
 
  • #4
Well no not exactly. [tex]e^{2-3x}>4[/tex] means [tex]ln(e^{2-3x})>ln(4)[/tex]

So you just need to solve [tex]2-3x>ln(4)[/tex]
 
  • #5
no ide bro... sorry
 
  • #6
EL ALEM said:
Forget that, I figured it out. I started it off kinda wrong.

lasner12 said:
no ide bro... sorry
What language is this?
 
  • #7
1337 speak :tongue:

coz he's leet
 

1. What is a logarithmic equation?

A logarithmic equation is an equation that contains logarithmic functions, which are the inverse of exponential functions. In other words, a logarithmic equation is used to solve for the power or exponent that a base number needs to be raised to in order to equal a given number.

2. How do I solve a logarithmic equation?

To solve a logarithmic equation, you need to isolate the logarithmic function on one side of the equation and the numerical value on the other side. Then, you can use the properties of logarithms to simplify the equation and solve for the variable.

3. What are the properties of logarithms?

The three main properties of logarithms are:

  • Product Property: logb(xy) = logb(x) + logb(y)
  • Quotient Property: logb(x/y) = logb(x) - logb(y)
  • Power Property: logb(xn) = n*logb(x)

4. What are common bases for logarithmic equations?

The two most common bases for logarithmic equations are base 10 (log10) and base e (ln). Base 10 is typically used in everyday calculations, while base e is used in more advanced mathematical equations.

5. Can logarithmic equations be used in real-life situations?

Yes, logarithmic equations have many applications in real-life situations, such as measuring the magnitude of earthquakes, measuring sound intensity, and calculating the pH level of a solution. They are also used in finance and economics to calculate compound interest and growth rates.

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