Solve for x log base 5 of 125^x=-3

Problem

(log_5)(125)=−3

Solution

1. Apply the power property of logarithms, which states that (log_b)(ap)=p*(log_b)(a)

(log_5)(125)=x*(log_5)(125)

2. Evaluate the logarithm by expressing 125 as a power of 5

125=5

3. Substitute the power back into the logarithmic expression.

(log_5)(5)=3

4. Rewrite the equation using the evaluated logarithm.

x⋅3=−3

5. Solve for x by dividing both sides of the equation by 3

x=(−3)/3

x=−1

Final Answer

(log_5)(125)=−3⇒x=−1

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