Math Problem Statement

Write as a logarithmic equation. 3 squaredequals9 Question content area bottom Part 1 The logarithmic form is    enter your response here. ​(Use integers or fractions for any numbers in the​ expression.)

Solution

To write the equation 32=93^2 = 9 in logarithmic form, recall that an equation in the form ax=ba^x = b can be rewritten as loga(b)=x\log_a(b) = x.

Given: 32=93^2 = 9

This translates to: log3(9)=2\log_3(9) = 2

So, the logarithmic form is: log3(9)=2\log_3(9) = 2

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:

  1. How would you express 43=644^3 = 64 in logarithmic form?
  2. What is the logarithmic form of 25=322^5 = 32?
  3. How can you rewrite 10x=100010^x = 1000 using logarithms?
  4. If log5(125)=3\log_5(125) = 3, what is the equivalent exponential form?
  5. How do logarithms help solve exponential equations?

Tip: Logarithms are essentially the inverse of exponents, so they help "undo" exponentiation by determining the power needed to reach a certain number.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

a^x = b can be written as log_a(b) = x

Theorems

Inverse property of exponents and logarithms

Suitable Grade Level

Grades 8-10