Subject: Mathematics
Book: Maths Mastery
Log inequalities like log(x) > 2 or log₂(x–1) ≤ 3 require understanding domain (x>0 for log base 10, x–1>0 for log₂) and exponential transformations. For log(x)>2, rewrite as x>10²=100. Solve carefully, checking intervals against log domain constraints. More complex expressions may involve combining log properties or adding constants. Log inequalities arise in pH ranges, decibel thresholds, or exponential growth constraints. Systematic approach ensures correct intervals, avoiding extraneous solutions from domain missteps.
If the average of five consecutive odd numbers is 25, what is the largest number?
View QuestionIf x + y = 10 and xy = 21, what is the value of x³ + y³?
View QuestionIf the probability of an event is 1/4, what is the probability of its complement?
View QuestionA man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?
View QuestionA number is increased by 20% and then decreased by 20%. What is the net change?
View QuestionWhat is the value of log₃(27)?
View QuestionWhat is the cube root of 729?
View QuestionWhat is the probability of drawing an ace from a standard deck of 52 cards?
View QuestionWhat is the probability of drawing a king from a standard deck of 52 playing cards?
View QuestionWhat is the sum of all even numbers between 1 and 50?
View Question