Solve for x log base 4 of 16=x

Problem

(log_4)(16)=x

Solution

1. Identify the logarithmic equation in the form (log_b)(y)=x where the base b=4 and the argument y=16

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

(log_4)(16)=x⇔4=16

3. Express the number 16 as a power with a base of 4 to make the bases on both sides of the equation match.

4=4

4. Solve for x by equating the exponents, since the bases are now identical.

x=2

Final Answer

(log_4)(16)=2

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