Rewrite as an equation.
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and does not equal , then is equivalent to .
Create equivalent expressions in the equation that all have equal bases.
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
The variable is equal to .
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Algebra
Evaluate log base 3 of 81
Step 1
Rewrite as an equation.
Step 2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and does not equal , then is equivalent to .
Step 3
Create equivalent expressions in the equation that all have equal bases.
Step 4
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
Step 5
The variable is equal to .
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What is Log Base 3 of 81?
log3(81) = 4
How to Find log3(81)? - Work with Steps
The below is the work with steps to find what is log base 3 of 81 shows how the input values are being used in the log base 3 functions. Formula:
logb(x) = y, if by = xInput:
x = 81
b = 3Solution:
y = log3 81
= log3 34
= 4 log3 3 = 4 x 1
log3 81 = 4
log3(81) = 4
Explanation:
Since #81# is much larger than #3#, our answer will be a decimal, so let's think of this problem in the opposite sense: #log_3(81)#. #3^4 = 81#, so #log_3(81) = 4#.
Using the law of exponents, we know that if #a^m = n#, then #n^(1/m) = a#. So using this rule, we know that #81^(1/4) = 3#, so #log_81(3)=1/4#
Here is the answer to questions like: Log base 3 of 81? or what is the base 3 log of 81?
Use our | Log3 calculator to find the logarithm of any positive number for any number base you enter.
What is logarithm?
A logarithm is the power to which a number must be raised in order to get some other number. In other words, the logarithm tells us how many of one number should be multiplied to get another number.
For example:
- The base 2 logarithm of 4 is 2, because 2 raised to the power of 2 is 4:
- log3 9 = 2, because 32 = 9
This is an example of a base-3 logarithm. We call it a base-3 logarithm because 3 is the number that is raised to a power.
The most common logarithms are natural logarithms and base 10 logarithms. There are special notations for them:
- A base 10 log is written simply log.
- A natural logarithm is written simply as ln.
So, the notation log alone means base ten logarithm and notation ln, means natural log.
Basic Log Rules
- logb(x·y) = logb(x) + logb(y)
- logb(x/y) = logb(x) - logb(y)
- logb(xy) = y·logb(x)
- logb(x) = logk(x)/logk(b)
Log Calculator
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