Important Properties of Exponential and Logarithmic Functions

Solving exponential and logarithmic expressions exponentially:

Examples

1.    Find the value of 4^x when x= 4.

Solution

4^x =4⁴ = 4 x 4 x 4 x 4=256

2.    If it is given that log₂12 = 2^3.585, then 12= 2^k and k=?

Solution

k = 3.585 becauselog₂12 = 2^3.585. Therefore, using the property of exponents 12=23.585 comparing it with 12=2^k , k=3.585.

Try this problem

1.    Log₄64 = ?

Answer:

Let Log₄64 = a
Then 64 = = 4³
Hence a=3.