Express the equation in logarithmic form.
(a)
ex = 9
  
Incorrect: Your answer is incorrect.
(b)
e7 = y

Let's convert these exponential equations into logarithmic form. 

### (a) \( e^x = 9 \)

The logarithmic form of the equation \( e^x = 9 \) is:

\[
x = \ln(9)
\]

This is because logarithms express the exponent to which the base \( e \) must be raised to produce 9.

### (b) \( e^7 = y \)

The logarithmic form of the equation \( e^7 = y \) is:

\[
7 = \ln(y)
\]

This expresses the idea that \( 7 \) is the exponent to which \( e \) must be raised to produce \( y \).

Would you like more details on how logarithmic conversion works, or have any questions about these?

Here are 5 related questions to deepen your understanding:
1. How would you express \( a^x = b \) in logarithmic form for any base \( a \)?
2. What is the relationship between natural logarithms and the constant \( e \)?
3. Can logarithmic functions handle negative numbers?
4. How would you solve \( \ln(x) = 3 \) for \( x \)?
5. How can you differentiate \( \ln(x) \) in calculus?

**Tip**: Remember that natural logarithms use base \( e \), where \( e \approx 2.718 \).

Express the equation in logarithmic form.
(a)
ex = 9
(b)
e7 = y

Learn how to convert the exponential equations e^x = 9 and e^7 = y into their logarithmic forms using natural logarithms. This guide covers key mathematical concepts like logarithms, exponential equations, and their relationship, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation