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Chapter 3: Problem 63

Write the exponential equation in logarithmic form. $$e^{-0.9}=0.406 \ldots$$

Short Answer

Expert verified
The logarithmic form of the given equation is \( \log_{e} 0.406 \ldots = -0.9\)

Step by step solution

01

Identify the Base, Exponent and the Result of the Exponential Equation

Looking at the equation \(e^{-0.9}=0.406 \ldots\), \(e\) is the base, -0.9 is the exponent (which is our b in this case), and 0.406 ... is the result (which is our c).
02

Convert to Logarithmic Form Using Conversion Rule

We use the conversion rule for exponential and logarithmic forms, \(a^{b}=c\) implies \( \log_{a} c = b\). Thus, the given equation in logarithmic form is \( \log_{e} 0.406 \ldots = -0.9\)

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Most popular questions from this chapter

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