Logarithm Formulas

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 ?

Solution:

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

Solution:

Using the logarithm property,

\log_{a}x+\log_{a}b=\log_{a}(x.b)
\log_{5}(x.2)=3
x.2=5^3
x.2=125
x=\frac{125}{2}=62.5

Question: 4 Evaluate the value of x in the equation \log_{3}x+\log_{3}2=1

Solution:

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

Solution:

Convert the equation to exponential form according to the natural logarithm,

e^3 = 2x + 1

\frac{(e^3-1)}{2}

So, x ≈ 3.1945