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- Logarithmic functions
For the following exercises, rewrite each equation in logarithmic form.
For the following exercises, solve for
by converting the logarithmic equation to exponential form.
For the following exercises, use the definition of common and natural logarithms to simplify.
Numeric
For the following exercises, evaluate the base
logarithmic expression without using a calculator.
For the following exercises, evaluate the common logarithmic expression without using a calculator.
For the following exercises, evaluate the natural logarithmic expression without using a calculator.
Technology
For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth.
Extensions
Is
in the domain of the function
If so, what is the value of the function when
Verify the result.
No, the function has no defined value for
To verify, suppose
is in the domain of the function
Then there is some number
such that
Rewriting as an exponential equation gives:
which is impossible since no such real number
exists. Therefore,
is
not the domain of the function
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Is there a number
such that
If so, what is that number? Verify the result.
Yes. Suppose there exists a real number
such that
Rewriting as an exponential equation gives
which is a real number. To verify, let
Then, by definition,
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Real-world applications
The exposure index
for a 35 millimeter camera is a measurement of the amount of light that hits the film. It is determined by the equation
where
is the “f-stop” setting on the camera, and
is the exposure time in seconds. Suppose the f-stop setting is
and the desired exposure time is
seconds. What will the resulting exposure index be?
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Refer to the previous exercise. Suppose the light meter on a camera indicates an
of
and the desired exposure time is 16 seconds. What should the f-stop setting be?
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The intensity levels
I of two earthquakes measured on a seismograph can be compared by the formula
where
is the magnitude given by the Richter Scale. In August 2009, an earthquake of magnitude 6.1 hit Honshu, Japan. In March 2011, that same region experienced yet another, more devastating earthquake, this time with a magnitude of 9.0.
How many times greater was the intensity of the 2011 earthquake? Round to the nearest whole number.
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Questions & Answers
how does the planets on our solar system orbit
how many Messier objects are there in space
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
why the moon is always appear in an elliptical shape
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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