Logarithm - examples
- Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
- Water lilies
Water lilies are growing on the pond and their number is doubled every day. The whole layer is covered in 12 days. How many days will it cover 8 layers?
Crystal grows every month 2.2 promile of its mass. For how many months to grow a crystal from weight 160 g to 311 g?
- When will I be a millionaire?
Shawn monthly send 220 euros to the bank, which he deposits bear interest of 2.4% p.a. Calculate how many months must Shawn save to save 1000000 euros? Inflation, interest rate changes or bank failures ignore.
- Compound interest
Calculate time when deposit in the bank with interest 2.5% p.a. doubles.
How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
The population grew in the city in 10 years from 42000 to 54500. What is the average annual percentage increase of population?
- Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
If ?, then n is:
Calculate what member of the sequence specified by ? has value 86.
- Future of libraries
You know that thanks to the Internet, electronic communications and developing online resources on the Internet annually declining number of traditional readership by 17%. These deal is irreversible evolutionary shift from old books from libraries to immed
The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years?
- Half life
Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes.
- Computer revolution
When we started playing with computers, the first processor, which I remember was the Intel 8080 from 1974, with the performance of 0.5 MIPS. Calculate how much percent a year rose CPU performance when Intel 486DX from 1992 has 54 MIPS. What
- Seating rules
In a class are 24 seats but in 7.B class are only 18 students. How many ways can student seat? (The class has 12 benches. A bench is for a pair of students.) Result (large number) logarithm and thus write down as powers of 10.
The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
- Logarithmic equation
Solve equation: log33(3x + 21) = 0
- Exponential equation
In the set R solve the equation: ?
- To the cinema
Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
After 548 hours decreases the activity of a radioactive substance to 1/9 of the initial value. What is the half-life of the substance?