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- Exponential and logarithmic
- 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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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