Solve for x log base x of 125=3

Problem

(log_x)(125)=3

Solution

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

x3=125

2. Identify the value of 125 as a power of a base, noting that 5×5×5=125

x3=5

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

√(3,x3)=√(3,125)

4. Simplify the expression to find the final value.

x=5

Final Answer

(log_x)(125)=3⇒x=5

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