Solve for x log of x=-3

Problem

(log_)(x)=−3

Solution

1. Identify the base of the logarithm. In most contexts, (log_)() without a specified base refers to the common logarithm, which has a base of 10

2. Rewrite the logarithmic equation in its equivalent exponential form. The definition states that (log_b)(y)=x is equivalent to bx=y

10(−3)=x

3. Evaluate the power of 10 to find the value of x A negative exponent indicates a reciprocal.

x=1/10

4. Simplify the fraction by calculating the denominator.

x=1/1000

5. Convert to decimal form if necessary.

x=0.001

Final Answer

(log_)(x)=−3⇒x=0.001

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