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August 3, 2023
When the power of a number must be raised in order to get some other number known as Logarithm. Here on this page, you will get Logarithm Formulas which will help you to Solve Logarithms based Questions easily.
\log_{b}y=x
Logarithms are the power to which a number is raised to achieve some other number.
Logarithm with base 10 is Common logarithm.
It is expressed as log10 X, and if any expression is not given with the base, then the base 10 is considered.
Logarithm with base e is Natural Logarithm.
It is expressed as loge X.
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Question: 1 Calculate the antilog of 3.6552.
Solution:
As we know that antilog is the inverse of the logarithm. so, it is clear that we are going to find the number whose logarithm is 3.6552
From the antilog table, we would find the value corresponding to row 65 and column 5 is 4508.
The mean difference column for the value 2 is 2.
Adding these two values, we have 4518 + 2 = 4520.
The decimal point is placed in 3 + 1 = 4 digits from the left. So, antilog 3.6552 = 4520.0
Question: 2 What will the value of x in the equation 2^x=16 ?
In logarithm notation: \log_{2}16=x
2^4=16\log_{2}(2^4)
x=4
Question: 3 Evaluate the value of x in the equation: \log_{5}x+\log_{5}2=3
Using the logarithm property,
\log_{a}x+\log_{a}b=\log_{a}(x.b)\log_{5}(x.2)=3x.2=5^3x.2=125x=\frac{125}{2}=62.5
Question: 4 Evaluate the value of x in the equation \log_{3}x+\log_{3}2=1
Using the logarithm property,\log_{a}x-\log_{a}b=\log_{a}(\frac{x}{b})\log_{3}(\frac{x}{2}=1
\frac{x}{2}=3^1\frac{x}{2}=3
To solve for x, multiply both sides by 2:x=6
Question: 5 Solve for x: ln(2x + 1) = 3
Convert the equation to exponential form according to the natural logarithm,
So, x ≈ 3.1945
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