Formulas For Logarithm

Formulas for Logarithm

• log_x X= 1
• log_a 1= 0
• a log^log_ax =X
• log_ax =  \frac{1}{log_x a} \
• log_a(x ^p) = p(log _ax)
• log_a x = \frac{log_{10} X}{log_{10} a} \
• log_a \frac{x}{y} \ = log_a X- log_a Y
• log_a (xy)= log_aX+ log_aY

Value of log(2 to 10): Remember

• Log 2 = 0.301
• Log 3 = 0.477= 0.48
• Log 4 = 0.60
• Log 5 = 0.698 = 0.7
• Log 6 = 0.778 = 0.78
• Log 7 = 0.845 = 0.85
• Log 8 = 0.90
• Log 9 = 0.954= 0.96
• Log 10 = 1

Logarithm Formulas (Antilog):

• An antilog is the inverse function of a logarithm.
  log(b) x = y means that antilog (b) y = x.
• The best way to understand any problem is by having a look at the Solved Example.
• We are going to do the same here, and we are going to understand the Antilog problem by Solved Example.

Question:   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 the 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