Logarithms - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams
Logarithms made easy
Logarithms are an important topic for entrance exams and placement tests, but many
students find them confusing. In this video, we will make this topic easy to
understand and solve all your confusions.
Before we begin with the questions, it is important to understand the basics of
this chapter. For example, if we have 5 raised to some power x, and the outcome is
25, then x is 2. Similarly, if we have 7 raised to some power x, and the outcome is
49, then x is 2 as well.
The logarithmic conversion is easy to understand. Log x to the base a is the
exponent of a, where the final result is x. This conversion can be used to convert
an exponent to a logarithm or vice versa.
Exponential to logarithmic: loga(xy) = y * loga(x)
Logarithmic to exponential: aloga(x) = x
Knowing these conversions will make it easy to solve logarithmic equations. For
example, if we have am = x, then loga(x) = m.
The logarithmic value of 1 is always 0, regardless of the base. For example,
log2(1) = 0 and log3(1) = 0.
The product rule of logarithms is loga(xy) = loga(x) + loga(y).
If we have loga(a) = 1, then loga(ax) = x and loga(loga(x)) = loga(x).
Remember that the base of the logarithm stays the same, and the positions of x and
m interchange when converting from exponential to logarithmic form or vice versa.
Quotient Rule
The quotient rule states that log of x by y to the base a is equal to log x by log
x to base a minus log y.
It is a common mistake among students to get this wrong, so pay attention to it.
Log Power
Log power is another important concept to know. It makes solving many questions
easier.
For example, if there is a power to the base and the number is without power, we
use the formula:
log x to the power a power b = log x to the base a plus log b to the base a
Power to Power Rule
If there is a power to the power, we use the formula:
log x to the power a to the power b = b times log x to the base a
Changing the Base
To change the base of a logarithm, we use the formula:
log a to the base b = log c to the base b divided by log c to the base a
Sample Questions
Can you write 81 as 3 to the power 4? Yes, so we can write this as log 3 to base 3
power 4.
Logarithms made easy
Logarithms are an important topic for entrance exams and placement tests, but many
students find them confusing. In this video, we will make this topic easy to
understand and solve all your confusions.
Before we begin with the questions, it is important to understand the basics of
this chapter. For example, if we have 5 raised to some power x, and the outcome is
25, then x is 2. Similarly, if we have 7 raised to some power x, and the outcome is
49, then x is 2 as well.
The logarithmic conversion is easy to understand. Log x to the base a is the
exponent of a, where the final result is x. This conversion can be used to convert
an exponent to a logarithm or vice versa.
Exponential to logarithmic: loga(xy) = y * loga(x)
Logarithmic to exponential: aloga(x) = x
Knowing these conversions will make it easy to solve logarithmic equations. For
example, if we have am = x, then loga(x) = m.
The logarithmic value of 1 is always 0, regardless of the base. For example,
log2(1) = 0 and log3(1) = 0.
The product rule of logarithms is loga(xy) = loga(x) + loga(y).
If we have loga(a) = 1, then loga(ax) = x and loga(loga(x)) = loga(x).
Remember that the base of the logarithm stays the same, and the positions of x and
m interchange when converting from exponential to logarithmic form or vice versa.
Quotient Rule
The quotient rule states that log of x by y to the base a is equal to log x by log
x to base a minus log y.
It is a common mistake among students to get this wrong, so pay attention to it.
Log Power
Log power is another important concept to know. It makes solving many questions
easier.
For example, if there is a power to the base and the number is without power, we
use the formula:
log x to the power a power b = log x to the base a plus log b to the base a
Power to Power Rule
If there is a power to the power, we use the formula:
log x to the power a to the power b = b times log x to the base a
Changing the Base
To change the base of a logarithm, we use the formula:
log a to the base b = log c to the base b divided by log c to the base a
Sample Questions
Can you write 81 as 3 to the power 4? Yes, so we can write this as log 3 to base 3
power 4.
