Math Problem Statement

Write as a logarithmic equation 10^5=100,000

Solution

To express the equation 105=100,00010^5 = 100,000 as a logarithmic equation, we can use the definition of a logarithm.

The general form of a logarithmic equation is:

logb(x)=yif and only ifby=x\log_b(x) = y \quad \text{if and only if} \quad b^y = x

Here, bb is the base, yy is the exponent, and xx is the result.

Given 105=100,00010^5 = 100,000, this is equivalent to:

log10(100,000)=5\log_{10}(100,000) = 5

This is the logarithmic form of the equation.

Would you like more details or explanations?
Here are 5 related questions:

  1. What is the logarithmic form of 23=82^3 = 8?
  2. How do you convert from a logarithmic form to an exponential form?
  3. What does the logarithm represent in real-world contexts?
  4. What is the difference between common logarithms and natural logarithms?
  5. How can we solve logarithmic equations?

Tip: Remember that logarithms and exponents are inverses of each other, so they can often be converted back and forth easily!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

log_b(x) = y if and only if b^y = x

Theorems

Logarithm-Exponent Inverse Property

Suitable Grade Level

Grades 8-10