First, you should know all the formulas related to the logarithm.

Let us take some examples:

1. Find the values of the log729

Solu: Let A = log 729

=> A = log (9 * 9 * 9)

=> A = log (3 * 3 * 3 * 3 * 3 * 3)

=> A = log 3⁶

=> A = 6 * log 3

=> A = 6 * 0.4771      {Since log 3 = 0.4771}

=> A = 2.8626

So, log 729 = 2.8626

2. If log (x - y)/4 = (1/2) * (log x + log y), then find the value of  x/y + y/x

Solu: 

Given, log (x - y)/4 = (1/2) * (log x + log y)

=> log (x - y)/4 = (1/2) * log (x*y)

=> log (x - y)/4 = log (x*y)^1/2

=> (x - y)/4 = (xy)^1/2

Take square on both side, we get

=> (x - y)² /16 = xy

=> (x² + y² - 2xy)/16 = xy

=> (x² + y² - 2xy)/xy = 16

=> x² /xy + y² /xy - 2xy/xy = 16

=> x/y + y/x - 2 = 16

=> x/y + y/x = 16 + 2

=> x/y + y/x = 18

So, in this way, we solve logarithm problems.