Math Problem Statement

Rewrite the following log equations in exponential form: a) log2(1) = 0 b) log(229) = x c) ln(x) = -1

Solution

Here are the rewritten logarithmic equations in exponential form:

a) log2(1)=0\log_2(1) = 0
Exponential form: 20=12^0 = 1

b) log(229)=x\log(229) = x
Exponential form: 10x=22910^x = 229
(Assuming the base is 10, as none is specified.)

c) ln(x)=1\ln(x) = -1
Exponential form: e1=xe^{-1} = x

Let me know if you'd like further clarification or additional details!

Related Questions:

  1. How do you convert between logarithmic and exponential forms?
  2. What is the significance of the natural logarithm (ln\ln)?
  3. How do different logarithmic bases (e.g., base 2, base 10) affect calculations?
  4. Can logarithmic equations with unknown bases be solved?
  5. How are logarithmic functions used in real-world applications?

Tip: Remember that ln(x)\ln(x) always has a base of ee (approximately 2.718), which is crucial when converting it to exponential form.

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Math Problem Analysis

Mathematical Concepts

Logarithmic Functions
Exponential Functions
Natural Logarithms

Formulas

log_b(a) = c is equivalent to b^c = a
ln(x) = c is equivalent to e^c = x

Theorems

Properties of Logarithms and Exponentials

Suitable Grade Level

Grades 9-12