Question

Solve for t: 5=e7t
.(1 point)
Responses

ln57
Start Fraction l n 5 over 7 End Fraction

57
Start Fraction 5 over 7 End Fraction

ln(57)
l n left parenthesis Start Fraction 5 over 7 End Fraction right parenthesis

ln5

Answer 1

To solve the equation \( 5 = e^{7t} \), we can use the natural logarithm (ln).

1. Take the natural logarithm of both sides:
\[
\ln(5) = \ln(e^{7t})
\]

2. Using the property of logarithms \( \ln(e^x) = x \), we simplify the right side:
\[
\ln(5) = 7t
\]

3. Now, solve for \( t \):
\[
t = \frac{\ln(5)}{7}
\]

So the answer is:
\[
\frac{\ln(5)}{7}
\]

This corresponds to the option you presented:
\[
\text{Start Fraction } \ln(5) \text{ over } 7 \text{ End Fraction}
\]