Express the equation in logarithmic form:
(a) is equivalent to . Then

and

(b) is equivalent to . Then

and

Ask by Rogers Colon. in the United States

Mar 28,2025

Question

Express the equation in logarithmic form:
(a) is equivalent to . Then

and

(b) is equivalent to . Then

and

Ask by Rogers Colon. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

(a)
- Start with the equation: $$ e^x = 2 $$.
- Take the natural logarithm of both sides:
  $$
  \ln\left(e^x\right)=\ln(2)
  $$
- Using the property $$\ln\left(e^x\right)=x$$, we obtain:
  $$
  x = \ln(2)
  $$
- Writing in the form $$\ln A = B$$, we have:
  $$
  \ln(2)=x
  $$
  Thus, 
  $$
  A=2 \quad \text{and} \quad B=x.
  $$

(b)
- Start with the equation: $$ e^5=x $$.
- Take the natural logarithm of both sides:
  $$
  \ln\left(e^5\right)=\ln(x)
  $$
- Using the property $$\ln\left(e^5\right)=5$$, we obtain:
  $$
  5 = \ln(x)
  $$
- Writing in the form $$\ln C = D$$, we have:
  $$
  \ln(x)=5
  $$
  Thus,
  $$
  C=x \quad \text{and} \quad D=5.
  $$
(a) $$ A = 2 $$ and $$ B = x $$ (b) $$ C = x $$ and $$ D = 5 $$

Express the equation in logarithmic form:
(a) is equivalent to . Then

and

(b) is equivalent to . Then

and

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Algebra Questions

Express the equation in logarithmic form: (a) is equivalent to . Then and (b) is equivalent to . Then and

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Algebra Questions

Express the equation in logarithmic form:
(a) is equivalent to . Then

and

(b) is equivalent to . Then

and