Evaluate log base 16 of 4

Problem

(log_16)(4)

Solution

1. Identify the logarithmic expression as an equation where x is the value we want to find.

(log_16)(4)=x

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(y)=x⇔bx=y

16=4

3. Express both sides of the equation using a common base, which in this case is 4

(4)x=4

4. Apply the power of a power rule (am)n=a(m⋅n) to simplify the left side.

4(2*x)=4

5. Equate the exponents since the bases are now identical.

2*x=1

6. Solve for x by dividing both sides by 2

x=1/2

Final Answer

(log_16)(4)=1/2

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