Use properties of logarithms to evaluate the expression.

Ask by Pope Schmidt. in the United States

Jan 24,2025

Question

Use properties of logarithms to evaluate the expression. $$ \ln e^{-4}-\ln e^{-\frac{3}{4}} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \ln(e^{-4})-\ln(e^{-\frac{3}{4}}) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\ln{\left(e^{-4}ight)}-\ln{\left(e^{-\frac{3}{4}}ight)}$$
- step1: Simplify the expression:
  $$-4-\ln{\left(e^{-\frac{3}{4}}ight)}$$
- step2: Simplify the expression:
  $$-4-\left(-\frac{3}{4}ight)$$
- step3: Remove the parentheses:
  $$-4+\frac{3}{4}$$
- step4: Reduce fractions to a common denominator:
  $$-\frac{4	imes 4}{4}+\frac{3}{4}$$
- step5: Transform the expression:
  $$\frac{-4	imes 4+3}{4}$$
- step6: Multiply the numbers:
  $$\frac{-16+3}{4}$$
- step7: Add the numbers:
  $$\frac{-13}{4}$$
- step8: Rewrite the fraction:
  $$-\frac{13}{4}$$
The expression $$ \ln e^{-4}-\ln e^{-\frac{3}{4}} $$ simplifies to $$ -\frac{13}{4} $$ or $$ -3\frac{1}{4} $$ or $$ -3.25 $$.
The expression simplifies to $$ -3.25 $$.

Use properties of logarithms to evaluate the expression.

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