- #1
scientifico
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Homework Statement
3 - 3^(x+1) < 5^x - 15^x
3(1-3^x) < 5^x(1-3^x)
Do I have to impose 1-3^x > 0 ?
It results x<0 and x>log(5,3) but book has written 0 < x < log(5,3) where did I wrong ?
Logarithm Inequality: Solving 3(1-3^x) < 5^x(1-3^x)
- Thread starter scientifico
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- Inequality Logarithm
In summary, a logarithm inequality is an inequality that contains a logarithm function, where the goal is to solve for the value of the variable that satisfies the inequality. To solve a logarithm inequality, you must isolate the logarithmic term and use logarithm rules and algebraic techniques. The inequality symbol (<, >, ≤, ≥) in a logarithm inequality indicates the relationship between the two sides. While a calculator can be helpful, it is not recommended to solely rely on it for solving logarithm inequalities. Real-life applications of logarithm inequalities can be found in various fields of science and finance.
3 - 3^(x+1) < 5^x - 15^x
3(1-3^x) < 5^x(1-3^x)
Do I have to impose 1-3^x > 0 ?
It results x<0 and x>log(5,3) but book has written 0 < x < log(5,3) where did I wrong ?
- #2
tiny-tim
Science Advisor
Homework Helper
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hi scientifico! 
(try using the X2 button just above the Reply box)
no, you can't do that, you don't know that it's true!
either you must deal separately with 1-3x > 0 and 1-3x < 0.
or just write (1-3x)(3-5x) < 0
(try using the X2 button just above the Reply box
)scientifico said:
no, you can't do that, you don't know that it's true!
either you must deal separately with 1-3x > 0 and 1-3x < 0.
or just write (1-3x)(3-5x) < 0
1. What is a logarithm inequality?
A logarithm inequality is an inequality that contains a logarithm function. This means that the variable in the inequality is inside the logarithm function, and the goal is to solve for the value of the variable that satisfies the inequality.
2. How do I solve a logarithm inequality?
To solve a logarithm inequality, you first need to isolate the logarithmic term on one side of the inequality. Then, you can use properties of logarithms and algebraic manipulations to solve for the variable. It is important to check any potential solutions in the original inequality to ensure they are valid.
3. What does the inequality symbol (<, >, ≤, ≥) mean in a logarithm inequality?
The inequality symbol in a logarithm inequality indicates the relationship between the two sides of the inequality. For example, < (less than) means that the value on the left side is smaller than the value on the right side.
4. Can I use a calculator to solve a logarithm inequality?
While a calculator can be helpful in evaluating logarithmic expressions, it is not recommended to solely rely on a calculator to solve logarithm inequalities. It is important to have an understanding of logarithm rules and algebraic techniques to accurately solve these types of inequalities.
5. What are some real-life applications of logarithm inequalities?
Logarithm inequalities can be used in various fields of science, such as physics, chemistry, and biology, to model and solve real-life problems. They are also commonly used in financial and economic calculations, such as determining interest rates and analyzing investment growth.
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