Logarithm - practice problems
A logarithm is the inverse operation of exponentiation, answering the question "to what power must the base be raised to obtain a given number." The logarithm of x to base b is written as log_b(x) and equals y if b^y = x. Common logarithms use base 10, while natural logarithms use base e (approximately 2.718). Logarithms transform multiplication into addition and division into subtraction, making complex calculations more manageable. They are essential in many scientific fields including chemistry (pH scale), seismology (Richter scale), and information theory. Students learn logarithm properties, solving logarithmic equations, and applications in exponential growth and decay.Directions: Provide a careful solution to each problem, showing all steps in your work.
Number of problems found: 101
- Simple interest pa
If a sum of money at a rate of simple interest, doubles in 8 years, then it will become 3 times in how many years? - GP - terms
Which term of the G.P., 2, 8, 32, ... up to n terms is 131072? - Doubling every day
If you start with 1 euro on day 1 and double your money daily, how many days before you get at least 1 million? - A town 3
A town with 12,000 people has been growing at a rate of 2.5% per year. How many years ago was the population 8,000? - Per annum
At a certain time, a sum becomes 4 times at the rate of 5% per annum. At what rate of simple interest the same sum becomes 8 times in the same duration - Compound interest
Joel borrowed $3208.5 on November 2, 2021, at 3.6% p.a. How many days would it take for him to repay the loan if he made a payment of $ 3,720.34? Round up to the nearest day. - Years 3
How long will it take for a given sum of money to triple itself at 20% annual compound interest? - Geometric series How many terms of the geometric series 8+4+2+1+0.5+... must be taken for the sum to get within 10 to the power minus 4 of its sum to infinity?
- Decadic logarithm
Log10 30 - log10 3 = X. Find X . - X-ray intensity
The intensity of X-ray radiation is reduced by half when passing through a 13.5 mm thick lead layer. Determine the thickness of the lead plate that will reduce the radiation intensity to one tenth of the original value. If we know that the intensity decre - Granulate for pH Adjustment
Bathing water should have a pH value in the range of 6.8 - 7.2. How much granulate should we add to increase the pH value from 6.2 to 7 if a dose of 100g/10m³ increases the pH by approx. 0.1? P.S. It's not 800 grams. - Student deposit years A student deposited €500 in a savings bank at 2.5% interest. In what time (in years) will he earn as much interest as he invested?
- Radiation shield
Determine what thickness of the shielding material will be required if we reduce the radiation to 3% of the original value if we know that a thickness of 6 mm will reduce the level of the same radiation by 9%. Round up to the whole value in millimeters (t - Robinson on the island
Robinson Crusoe came to the island with 4 grains of corn. How many years did it take him to grow enough grain for bread if he got 10 grains from one grain on average and he needed at least 1kg of bole for 1 bread, and 1 grain weighs about 0.2g? (assume on - Machine depreciation years
8% of the price of the machine is written off every year. In how many years will the price drop from 250,000 to 150,000? - Deposit double years The bank offers interest on the deposit of 4 percent per annum. In how many years will the deposit double?
- Geometric sequence terms
The two terms of the geometric sequence are a2=12 and a5=three halves. a) calculate the tenth term of the sequence. b) calculate the sum of the first 8 terms of the sequence. v) how many first terms of the sequence need to be added so that the sum is equa - Bernoulli trial
A used car saleswoman estimates that each time she shows a customer a car, there is a probability of 0.1 that the customer will buy the car. The saleswoman would like to sell at least one car per week. If showing a car is a Bernoulli trial with a probabil - The terms
The terms 1/64, 1/32, and 1/16 form a geometric progression (GP). If the sum of the GP is (2³6 – 2-6), find the number of terms. - Nitrogen gas
In a cylinder with a piston, there is nitrogen N2 with a volume of 5 liters, a temperature of 25 degrees Celsius, and a pressure of 200 kPa. We very slowly compress the gas in the cylinder to half its volume while its temperature does not change. Determin
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