What Is a Logarithm?
Read this topicExplanations 5
- (Video) Logarithms Explained by Steve Kelly on Ted-Ed In this video, we learn about the relationship between exponents and logarithms. Summary\large{\text{Summary}}Summary The i…
By Ben Ferrara, Alex Federspiel, Amy Feraco
- (Video) Logarithmic Functions by mathman1024 Here's a video by mathman1024 explaining logarithmic functions. Summary\large{\text{Summary}}Summary Remember that exponential funct…
By Alex Federspiel, Amy Feraco, Anusha Rahman
- We already know how to use power statements. These are written in the form: x=ayx=a^{y}x=ay As with every equation, we can change the subject of the equation to solve different …
By Shona, Alex Federspiel, Anusha Rahman
- We've learned a bit about exponents recently, from exponential decay, to solving exponential equations, to graphing exponential equations. Now, we'll dive into a similar, yet di…
By Tina Sindwani, Amy Feraco, Alex Federspiel, Anusha Rahman
- Logarithms We are quite familiar with exponents, so we are going to take this a step further and look at a new way to examine exponents! We have John Napier to thank for this co…
By Anusha Rahman
Problems 21
- A group of bacteria was observed to be at 130013001300 and grow at a rate of about 3.52%3.52\%3.52% per day. What is an equation for the bacteria's growth? How long will it take…
- A species of fish has an extremely long lifespan and rarely have children. If there are a total of 930930930 of this type of fish and their growth rate is 8.3%8.3\%8.3% each mon…
- A type of bacteria has a very high exponential growth rate of 76%76\%76% every hour. If there are 101010 bacteria, determine how many there will be in half a day. How long until…
- An island was recorded to have a population of 100100100 after 222 years. Then, after 666 years, it was recorded to have a population of 810081008100. Find the equation that rep…
- In 200820082008, Cooper bought a car for 36000\3600036000. It depreciates 12%12\%12% per year. What year will the car be worth 6000\60006000?
- The half-life of an isotope is 333 years. how many years would it take a 101010 mg sample to decay to 0.50.50.5 mg? Round to the nearest year.
- If 400400400 mg of ibuprofen decreases about 30%30\%30% every hour, how long would it take for 424242 mg to remain?
- Rewrite the equality 34=813^4=8134=81 using logarithms.
- Using logarithms, rewrite 105=100,00010^5=100,000105=100,000.
- Express the relation log2128=7\log_2 128=7log2128=7 in terms of powers?
- Rewrite the fact that log4256=4\log_{4}256=4log4256=4, in terms of exponents.
- If log7343=3\log_7 343=3log7343=3, then find a real number xxx such that 7x=3437^x = 3437x=343.
- Rewrite 10−3=0.00110^{-3}=0.00110−3=0.001 in terms of logarithms.
- What is log103\log 10^3log103?
- What is 10log510^{\log 5}10log5?
- If 6951.37\6951.376951.37 was put into your account at some unknown date and it's now 10166.30\10166.3010166.30. The interest rate is 7.7%7.7\%7.7% and it is compounded triannua…
- An unknown amount of money was placed in a bank account with a semiannual interest rate of 8.8%8.8\%8.8%. After 333 years, there's 3545.17\3545.173545.17 in the account. After t…
- An isotope decays exponentially. Suppose that after one minute, there are 101010 grams remaining, and after five minutes, there are 222 grams remaining. What is the half-life, i…
- Without performing any calculations, which of the following ranges contains log10756\log_{10}756log10756?
- Without performing any calculations, which of the following ranges contains log1093050\log_{10}93050log1093050?
- Let λ∈(0,1).\lambda \in (0, 1).λ∈(0,1). Find the value of limx→∞ln(xλ(x+1)λ−1)λx+(1−λ)(x+1).\lim_{x \rightarrow \infty}\frac{\ln\left(\frac{x^{\lambda}}{(x + 1)^{\lambda - 1}}…