Math Problem Statement

Write the exponential equation in logarithmic form.

103=1000log=3

Solution

To convert the given exponential equation to logarithmic form, follow these steps:

Given Exponential Equation:

103=100010^3 = 1000

Logarithmic Form:

log10(1000)=3\log_{10}(1000) = 3

Since log\log without a base is assumed to be base 10, we can simplify: log1000=3\log 1000 = 3

Would you like a step-by-step breakdown of the conversion process?


Here are five related questions to expand your understanding:

  1. Convert 25=322^5 = 32 to logarithmic form.
  2. Convert log216=4\log_2 16 = 4 to exponential form.
  3. Solve for xx in the equation 5x=1255^x = 125 using logarithms.
  4. What is the difference between natural logarithms (lnx\ln x) and common logarithms (logx\log x)?
  5. How do you evaluate logarithms without a calculator?

Tip: The logarithmic form of an equation helps in solving for exponents, making it useful in exponential growth, decay, and finance problems.

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Math Problem Analysis

Mathematical Concepts

Exponential Equations
Logarithms

Formulas

Exponential form: a^b = c
Logarithmic form: log_a(c) = b

Theorems

Change of base theorem

Suitable Grade Level

Grades 9-11