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Writing in logarithmic and exponential form Video Lecture - Engineering Mathematics
FAQs on Writing in logarithmic and exponential form Video Lecture - Engineering Mathematics
| 1. What is the logarithmic form of the exponential equation 2^x = 8? |  |
| 2. How can logarithmic form be used to solve exponential equations? | |
Ans. Logarithmic form can be used to solve exponential equations by taking the logarithm of both sides of the equation, isolating the variable on one side, and then evaluating the logarithm using the appropriate base.
| 3. How can exponential form be used to solve logarithmic equations? | |
Ans. Exponential form can be used to solve logarithmic equations by converting the equation to exponential form, isolating the variable on one side, and then evaluating the exponential expression using the appropriate base.
| 4. What is the relationship between logarithmic and exponential functions? | |
Ans. Logarithmic and exponential functions are inverses of each other. This means that if y = loga(x), then x = a^y. They essentially "undo" each other's operations.
| 5. How can logarithmic and exponential functions be applied in engineering mathematics? | |
Ans. Logarithmic and exponential functions are commonly used in engineering mathematics to model various phenomena, such as exponential growth or decay, signal processing, and circuit analysis. They are also used in solving problems related to exponential growth, interest rates, and logarithmic scales in engineering applications.
Text Transcript from Video
Voiceover:Rewrite the following
equation in logarithmic form.
So they wrote 100 is equal to 10
to the second power.
So if we wanna write the same
information, really, in logarithmic form,
we could say that the power that I need
to raise 10 to to get
to 100 is equal to 2,
or log base 10 of 100 is equal to 2.
Notice these are equivalent statements.
This is just in exponential form.
This is is logarithmic form.
This is saying that the power I need
to raise 10 to to get
to 100 is equal to 2.
Which is the same thing as saying
that 10 to the 2nd power is 100.
10 to the second power is 100.
And the way that I specify the base
is by doing this
underscore right over here.
So underscore 10, log base 10 of 100
is equal to 2.
Here they ask us to rewrite the following
equation in exponential form.
So this is log base 5 of 1 over 125
is equal to negative 3.
This is one way to
think about it is saying
the power that I need to raise 5
to to get to 1 over 125
is equal to negative 3
or that 5 to the negative 3 power is
equal to 1 over 125.
And we can verify that this has formatted
it the right way.
5 to the negative 3 power is 1 over 125.
The exact same truth about the universe,
just in different forms.
Logarithmic form and exponential form.
So let me check my answer
and make sure I got it right.
And I did.
equation in logarithmic form.
So they wrote 100 is equal to 10
to the second power.
So if we wanna write the same
information, really, in logarithmic form,
we could say that the power that I need
to raise 10 to to get
to 100 is equal to 2,
or log base 10 of 100 is equal to 2.
Notice these are equivalent statements.
This is just in exponential form.
This is is logarithmic form.
This is saying that the power I need
to raise 10 to to get
to 100 is equal to 2.
Which is the same thing as saying
that 10 to the 2nd power is 100.
10 to the second power is 100.
And the way that I specify the base
is by doing this
underscore right over here.
So underscore 10, log base 10 of 100
is equal to 2.
Here they ask us to rewrite the following
equation in exponential form.
So this is log base 5 of 1 over 125
is equal to negative 3.
This is one way to
think about it is saying
the power that I need to raise 5
to to get to 1 over 125
is equal to negative 3
or that 5 to the negative 3 power is
equal to 1 over 125.
And we can verify that this has formatted
it the right way.
5 to the negative 3 power is 1 over 125.
The exact same truth about the universe,
just in different forms.
Logarithmic form and exponential form.
So let me check my answer
and make sure I got it right.
And I did.
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About this Video
Mar 02, 2025
Last updated
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