Class 10 Exam > Class 10 Videos > Logarithmic Equations - Math, Class 10
Logarithmic Equations - Math, Class 10 Video Lecture
FAQs on Logarithmic Equations - Math, Class 10 Video Lecture
| 1. What is a logarithmic equation? |  |
Ans. A logarithmic equation is an equation in which the variable appears as an exponent of a logarithm. It can be solved by using logarithmic properties and techniques such as changing the base, using the inverse function, and simplifying the equation.
| 2. How do you solve logarithmic equations? | |
Ans. To solve a logarithmic equation, you need to isolate the logarithm on one side of the equation and then apply logarithmic properties to simplify it. After simplifying, you can solve for the variable by exponentiating both sides of the equation. Remember to check for extraneous solutions as well.
| 3. What are some common techniques used to solve logarithmic equations? | |
Ans. Some common techniques used to solve logarithmic equations include:
- Changing the base of the logarithm using the change of base formula.
- Applying the inverse function of logarithm, which is exponentiation.
- Simplifying the equation by using logarithmic properties such as product, quotient, and power rules.
- Checking for extraneous solutions by substituting the found values back into the original equation.
| 4. Can all logarithmic equations be solved algebraically? | |
Ans. Not all logarithmic equations can be solved algebraically. Some equations may have complex solutions or no real solutions. In such cases, numerical methods or approximation techniques may be used to estimate the solutions.
| 5. What are some real-life applications of logarithmic equations? | |
Ans. Logarithmic equations are used in various real-life applications, such as:
- Calculating the pH level in chemistry.
- Modeling population growth and decay.
- Analyzing sound and earthquake intensity using the Richter scale.
- Determining the amount of time needed for investments to double using compound interest formulas.
- Measuring the intensity of light using the decibel scale.
Text Transcript from Video
Convert log base
4 of 2 equals 1/2
into an exponential equation.
So a logarithm
literally tells you--
so if we were to just look
at this part right over here,
a logarithm is just saying,
tell me the exponent
that I would have
to raise my base to,
that I would have to
raise 4 to, to get to 2.
So tell me the
exponent that I would
have to raise it to to get to 2.
And so this equation written
as a logarithmic equation says,
I need to raise 4 to the
1/2 power in order to get 2.
So if I wanted to write it
as an exponential equation,
I could literally just
say, well, if I raise 4--
and that's this 4
right over here.
That's my base-- to this
exponent, to the 1/2 power,
then that is going
to be equal to 2.
And we're done.
We've written the same equation
as an exponential equation.
The value of a logarithm--
this is saying,
what do I get if I raise
4 to the 1/2 power?
I get 2 if I raise
4 to the 1/2 power.
This is saying, what power do I
have to raise 4 to to get to 2?
And then that is equal to 1/2.
So a logarithm is
saying, what power
do I have to raise
the base to to get
what's inside the logarithm?
This says, what do I get to
when I raise 4 to the 1/2 power?
4 of 2 equals 1/2
into an exponential equation.
So a logarithm
literally tells you--
so if we were to just look
at this part right over here,
a logarithm is just saying,
tell me the exponent
that I would have
to raise my base to,
that I would have to
raise 4 to, to get to 2.
So tell me the
exponent that I would
have to raise it to to get to 2.
And so this equation written
as a logarithmic equation says,
I need to raise 4 to the
1/2 power in order to get 2.
So if I wanted to write it
as an exponential equation,
I could literally just
say, well, if I raise 4--
and that's this 4
right over here.
That's my base-- to this
exponent, to the 1/2 power,
then that is going
to be equal to 2.
And we're done.
We've written the same equation
as an exponential equation.
The value of a logarithm--
this is saying,
what do I get if I raise
4 to the 1/2 power?
I get 2 if I raise
4 to the 1/2 power.
This is saying, what power do I
have to raise 4 to to get to 2?
And then that is equal to 1/2.
So a logarithm is
saying, what power
do I have to raise
the base to to get
what's inside the logarithm?
This says, what do I get to
when I raise 4 to the 1/2 power?
About this Video
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Oct 06, 2025
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