Logarithm

Law of Logarithm

Log_a¹ = 0

Log_a^m + log_aⁿ = log_a^{(m x n)}

Log_a^{b n} = n x log_a^b

Log_a^m – log_aⁿ = log_a(^m/n)

Example:-

1.   Write the following indices to logarithms form:-

a)   5² = 25

b)   164²

c)   125 = 5³

Answer:-

a)   Log₅²⁵ = 2

b)   Log₄¹⁶ =2

c)   Log₅¹²⁵ = 3

2.   Write is log₅⁶²⁵?

Log₅⁶²⁵ = ?

5^x = 625

5^x = 54

Log₅⁶²⁵ = 4

3.   Log₇7 + 4log₇^3-2log₇⁹

= 1 + log₇³⁴ – log₇⁹²

= 1 + log₇⁸¹ – log₇⁸¹

= 1

4.   Solve the equation:-

Log₃ (2 + x) = 4

Log₃⁴ = 2 + x

81 = 2 + x

81 – 2 + x

79 = x