Solve for x log base 2 of 16=x

Problem

(log_2)(16)=x

Solution

1. Identify the logarithmic equation in the form (log_b)(a)=x where the base b=2 and the argument a=16

2. Rewrite the equation in its equivalent exponential form using the definition bx=a

(log_2)(16)=x⇔2=16

3. Express the number 16 as a power of the base 2 to facilitate solving for the exponent.

16=2

4. Substitute the power back into the exponential equation.

2=2

5. Equate the exponents since the bases are the same.

x=4

Final Answer

(log_2)(16)=4

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