1 year, 6 months ago
via math-questions.com
What is a logarithm and what are some practical uses for it?
Many students have a difficult time grasping the concept of logarithms that is taught in algebra and never see a point in learning it. Can someone gives examples of why one should know this? What methods will make learning this easier? Will this ever be used in every day life?
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$1 Answer
A logarithm is basically another way of writing an exponential equation. If you have an equation of the form b^y=x you can rewrite it as log(base b)x = y. For example 3^y = 125 is the same as log(base 3)125 = y.
There are special rules for logarithms. The logarithm of a product is the same as the sum of the logarithms. For example, log(xy) = log(x)+log(y). The loqarithm of a quotient is the same as the difference of the logarithms. For example, log(x/y) = log(x)-log(y). A problem in the form of log(x)^y is the same as y*log(x). The exponent becomes the coefficient.
There are some practical uses of a logarithm and natural logarithm, which is logarithm to the base e, where e is approximately 2.718281828. If you have 1,000 in an account and want to know how long it will take for it to become 5,000 when you have 8% interest compounded 4 times per year, you can use a natural log to figure it out.
A=P*(1+r/n)e^(nt) where A= 5000, P = 1000, n=4 (number times per year compounded) and r = .08.
5000 = 1000(1+.08/4)e^(4t)
5= (1.02)e^(4t)
take the natural log of both sides (which is denoted as ln)
ln5= ln(1.02)e^(4t)
ln5/ln(1.02) = 4t
t= 20.32 years
There are special rules for logarithms. The logarithm of a product is the same as the sum of the logarithms. For example, log(xy) = log(x)+log(y). The loqarithm of a quotient is the same as the difference of the logarithms. For example, log(x/y) = log(x)-log(y). A problem in the form of log(x)^y is the same as y*log(x). The exponent becomes the coefficient.
There are some practical uses of a logarithm and natural logarithm, which is logarithm to the base e, where e is approximately 2.718281828. If you have 1,000 in an account and want to know how long it will take for it to become 5,000 when you have 8% interest compounded 4 times per year, you can use a natural log to figure it out.
A=P*(1+r/n)e^(nt) where A= 5000, P = 1000, n=4 (number times per year compounded) and r = .08.
5000 = 1000(1+.08/4)e^(4t)
5= (1.02)e^(4t)
take the natural log of both sides (which is denoted as ln)
ln5= ln(1.02)e^(4t)
ln5/ln(1.02) = 4t
t= 20.32 years
images:
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$Report Abuse
