Solve for x log base 5 of x=-3

Problem

(log_5)(x)=−3

Solution

1. Identify the logarithmic equation in the form (log_b)(x)=y where the base b=5 the argument is x and the result y=−3

2. Apply the definition of a logarithm to rewrite the equation in exponential form x=b^y

x=5^(−3)

3. Simplify the expression by applying the negative exponent rule a^(−n)=1/(a^n)

x=1/5^3

4. Evaluate the power in the denominator.

x=1/125

Final Answer

(log_5)(x)=−3⇒x=1/125

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