Question
Change the exponential statement to an equivalent statement involving a logarithm. The equivalent loganithmic statement is \( x=15 \) \( e^{x}=\ln 15^{\circ} \). (Type an equation.)
Ask by Osborne Carrillo. in the United States
Jan 17,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \ln(15) \)
Solution
To convert the exponential equation \( e^{x} = 15 \) to its equivalent logarithmic form, you can use the natural logarithm (denoted as \( \ln \)).
The logarithmic form of the equation \( e^{x} = 15 \) is:
\[
x = \ln(15)
\]
This equation states that \( x \) is the natural logarithm of 15.
**Final Answer:**
\[
x = \ln(15)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To convert the exponential statement \( e^{x} = \ln 15^{\circ} \) into a logarithmic one, we start from the general principle of logarithms, which states that if \( a^{b} = c \), then \( b = \log_{a} c \). In this case, we have: \( x = \log_{e}(\ln 15^{\circ}) \) So, the equivalent logarithmic statement is: \( x = \ln(\ln 15^{\circ}) \)
