Solve for x log base x of 8=3

Problem

(log_x)(8)=3

Solution

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

x3=8

2. Express the constant on the right side as a power with the same exponent as the left side.

x3=2

3. Solve for x by taking the cube root of both sides of the equation.

x=√(3,8)

4. Simplify the result to find the final value of x

x=2

Final Answer

(log_x)(8)=3⇒x=2

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