Solve for x log base x of 16=4

Problem

(log_x)(16)=4

Solution

1. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(a)=c⇔bc=a

x4=16

2. Express the constant 16 as a power with an exponent of 4 to match the left side of the equation.

x4=2

3. Solve for x by taking the fourth root of both sides, noting that the base of a logarithm must be positive and not equal to 1.

x=2

Final Answer

(log_x)(16)=4⇒x=2

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