Solve for x log base 3 of x=-3

Problem

(log_3)(x)=−3

Solution

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

2. Rewrite the equation in its equivalent exponential form using the definition ba=y

3(−3)=x

3. Evaluate the negative exponent by applying the rule n(−m)=1/(nm)

x=1/3

4. Simplify the denominator by calculating the power of 3.

x=1/27

Final Answer

(log_3)(x)=−3⇒x=1/27

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