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- Algebra and trigonometry
- Exponential and logarithmic
- Logarithmic functions
Key equations
| Definition of the logarithmic function |
For
if and only if
|
| Definition of the common logarithm |
For
if and only if
|
| Definition of the natural logarithm |
For
if and only if
|
Key concepts
- The inverse of an exponential function is a logarithmic function, and the inverse of a logarithmic function is an exponential function.
- Logarithmic equations can be written in an equivalent exponential form, using the definition of a logarithm. See
[link] .
- Exponential equations can be written in their equivalent logarithmic form using the definition of a logarithm See
[link] .
- Logarithmic functions with base
can be evaluated mentally using previous knowledge of powers of
See
[link] and
[link] .
- Common logarithms can be evaluated mentally using previous knowledge of powers of
See
[link]
.
- When common logarithms cannot be evaluated mentally, a calculator can be used. See
[link]
.
- Real-world exponential problems with base
can be rewritten as a common logarithm and then evaluated using a calculator. See
[link]
.
- Natural logarithms can be evaluated using a calculator
[link]
.
Section exercises
Verbal
What is a base
logarithm? Discuss the meaning by interpreting each part of the equivalent equations
and
for
A logarithm is an exponent. Specifically, it is the exponent to which a base
is raised to produce a given value. In the expressions given, the base
has the same value. The exponent,
in the expression
can also be written as the logarithm,
and the value of
is the result of raising
to the power of
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How can the logarithmic equation
be solved for
using the properties of exponents?
Since the equation of a logarithm is equivalent to an exponential equation, the logarithm can be converted to the exponential equation
and then properties of exponents can be applied to solve for
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Discuss the meaning of the natural logarithm. What is its relationship to a logarithm with base
and how does the notation differ?
The natural logarithm is a special case of the logarithm with base
in that the natural log always has base
Rather than notating the natural logarithm as
the notation used is
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Algebraic
For the following exercises, rewrite each equation in exponential form.
Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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