Rewriting and solving a real-world exponential model
The amount of energy released from one earthquake was 500 times greater than the amount of energy released from another. The equation
represents this situation, where
is the difference in magnitudes on the Richter Scale. To the nearest thousandth, what was the difference in magnitudes?
We begin by rewriting the exponential equation in logarithmic form.
Next we evaluate the logarithm using a calculator:
The amount of energy released from one earthquake was
times greater than the amount of energy released from another. The equation
represents this situation, where
is the difference in magnitudes on the Richter Scale. To the nearest thousandth, what was the difference in magnitudes?
The most frequently used base for logarithms is
Base
logarithms are important in calculus and some scientific applications; they are called
natural logarithms . The base
logarithm,
has its own notation,
Most values of
can be found only using a calculator. The major exception is that, because the logarithm of 1 is always 0 in any base,
For other natural logarithms, we can use the
key that can be found on most scientific calculators. We can also find the natural logarithm of any power of
using the inverse property of logarithms.
Definition of the natural logarithm
A
natural logarithm is a logarithm with base
We write
simply as
The natural logarithm of a positive number
satisfies the following definition.
For
We read
as, “the logarithm with base
of
” or “the natural logarithm of
”
The logarithm
is the exponent to which
must be raised to get
Since the functions
and
are inverse functions,
for all
and
for
Given a natural logarithm with the form
evaluate it using a calculator.
Press
[LN] .
Enter the value given for
followed by
[ ) ] .
Press
[ENTER] .
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
