Evaluate log base 2 of 512

Problem

(log_2)(512)

Solution

1. Identify the base and the argument of the logarithm. The base is 2 and the argument is 512

2. Rewrite the argument as a power of the base. We look for an exponent x such that 2^x=512

3. Calculate the powers of 2 to find the exponent: 2^1=2 2^2=4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256 2^9=512

4. Substitute the power back into the logarithmic expression: (log_2)(2^9)

5. Apply the logarithm property (log_b)(b^x)=x to simplify the expression.

Final Answer

(log_2)(512)=9

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