On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
I provided a link in post #5.Pranav-Arora said:Thanks Mark44 for your solution.
it worked for me.
And also thamks for notifying me, can you please provide me with a link where i can learn about the rules and regulations of board?
Logarithmic inequalities are mathematical expressions that involve logarithms and inequality symbols such as <, >, ≤, and ≥. They are used to compare two logarithmic expressions and determine which one is bigger or smaller.
To solve logarithmic inequalities, you need to isolate the logarithmic expression on one side of the inequality sign and the numerical expression on the other side. Then, you can use the properties of logarithms to rewrite the logarithmic expression in terms of the numerical expression. Finally, you can compare the numerical expressions to find the range of values that satisfy the inequality.
The common properties of logarithms used to solve logarithmic inequalities include the product rule, quotient rule, power rule, and change of base rule. These properties allow you to manipulate the logarithmic expressions and rewrite them in a simpler form.
The domain of a logarithmic inequality is the set of all real numbers that make the inequality true. This is because logarithmic functions are only defined for positive values, so the values that make the logarithmic expression positive must be included in the domain.
Logarithmic inequalities are used in various fields of science, such as biology, chemistry, and physics. They are also used in finance and economics to model growth rates and compound interest. In engineering, they are used to analyze complex systems and make predictions. In everyday life, logarithmic inequalities can be used to compare the sizes of quantities or determine the rate of change in a given situation.