Evaluate log base 2 of 32

Problem

(log_2)(32)

Solution

1. Identify the logarithmic expression as an equation where the base 2 raised to some power x equals 32

(log_2)(32)=x

2. Rewrite the equation in exponential form using the definition of a logarithm.

2=32

3. Express the number 32 as a power of 2 by identifying its prime factors.

32=2⋅2⋅2⋅2⋅2

32=2

4. Equate the exponents since the bases are now the same.

2=2

x=5

Final Answer

(log_2)(32)=5

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