# Logarithms

In Glogpedia

Last updated 4 years ago

Discipline:
Math
Subject:
Calculus
9,10,11,12

Why does the input have to be greater than 0???Because our base is always a positive number, it is impossible to get a negative answer when we raise the base to a power. Consider the log base 2 on the left <-----. Imagine we replace the input (16) with a variable. Is it possible to raise 2 to any power and have that answer be a negative number? No--- therefore the input has to be positive!This is always true.

Check out the video below on:log basics

Logarithms allow us to talk about really big numbers in a more friendly way. For example, we can talk about the number 100,000,000 by referencing how many times 10 has multiplied itself to give this result (8 times). This came in handy hisotrically as really big numbers were difficult to work with without calculators.Logarithms also allow us to determine to what power a number must be raised to produce a given quantity. For example 5 raised to what power equals 20?

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Logarithms

If the input is 1, why is the answer always 0???Imagine any logarithm that has an answer of 0. When we re-write that logarithm as an exponential expression, the exponent would be the answer of the logarithm (0). And anything raised to a 0 power equals 1. This would be the input of the logarithm.log_a_(x)=0a^0=xx=1

Properties

Why?

Uses

Example #1

Example

Check out the video below on:graphing

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