Solve for b log base b of 216=3

Problem

(log_b)(216)=3

Solution

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

b3=216

2. Identify the value of b by taking the cube root of both sides of the equation.

b=√(3,216)

3. Evaluate the cube root by recognizing that 216 is a perfect cube, specifically 6×6×6

b=6

Final Answer

(log_b)(216)=3⇒b=6

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