Algebra2D

Logarithms - Theory & Concepts - Logarithm Scale

Rules of logarithms, natural logs, change of base formula, and solving logarithmic and exponential equations.

Linear vs. Logarithmic Scale

Energy / Intensity Factor (

10^x

)x = 3.0

1100M

Linear Scale

Value:

1.0k

Notice how the linear bar barely moves for small values, then shoots off completely for large ones.

Logarithmic Scale (Base 10)

$\log_{10}(\text{Value}):$

3.0

The logarithmic scale grows proportionally to the exponent, compressing huge ranges into manageable numbers.

Order of Magnitude: An increase of $+1$ on a Base-10 logarithmic scale means the underlying value gets 10 times larger. An increase of $+2$ means it gets 100 times larger.

Richter Scale

A magnitude 6.0 earthquake has 10 times the wave amplitude of a 5.0.

Decibels (dB)

Every 10 dB increase represents a 10-fold increase in sound intensity.

pH Scale

A pH of 4 has 10 times the hydrogen ion concentration of pH 5.

Fundamentals - Theory & Concepts Fundamentals - Theory & Concepts - Absolute Value Exponents and Radicals - Theory & Concepts - Exponent Rules Exponents and Radicals - Theory & Concepts - Power Function

Linear vs. Logarithmic Scale

Linear Scale

Logarithmic Scale (Base 10)

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