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17 results for “base”

Formulae (14)

Change of Base Formula

\log_b(x) = \frac{\log_k(x)}{\log_k(b)}

Converts a logarithm from one base to another.

AlgebraBasic

Product of Powers

a^m \cdot a^n = a^{m+n}

Multiplying powers with the same base adds the exponents.

AlgebraBasic

Quotient of Powers

\frac{a^m}{a^n} = a^{m-n}

Dividing powers with the same base subtracts exponents.

AlgebraAdvanced

Change of Base

\log_b x = \frac{\log_k x}{\log_k b}

Convert a logarithm to a different base.

AlgebraBasic

Quotient of Powers

\frac{a^m}{a^n} = a^{m-n}

Divide powers with the same base by subtracting exponents.

Geometry & TrigonometryBasic

Area of a Triangle

A = \frac{1}{2} b h

Area of a triangle from base and height.

ChemistryBasic

pH

pH = -\log_{10}[H^+]

Acidity from hydrogen-ion concentration.

ChemistryBasic

pOH

pOH = -\log_{10}[OH^-]

Basicity from hydroxide-ion concentration.

ChemistryBasic

pH and pOH

pH + pOH = 14

Relationship between acidity and basicity at 25°C.

ChemistryAdvanced

Water Ion Product

K_w = [H^+][OH^-] = 10^{-14}

Self-ionization constant of water at 25°C.

Biology & Life SciencesIntermediate

GC Content

\%GC = \frac{G + C}{A + T + G + C} \times 100

Proportion of G and C bases in DNA.

Health & FitnessIntermediate

Ideal Body Weight (Devine)

IBW = 50 + 2.3(h - 60)

Devine formula for men (kg), height in inches; women use base 45.5.

EconomicsIntermediate

Consumer Price Index

CPI = \frac{\text{Basket now}}{\text{Basket base}}\times 100

Measures price levels relative to a base year.

Everyday MathBasic

Tip Amount

\text{Tip} = B \times r

Gratuity based on a bill amount.

Math Tricks (3)

Nikhilam (Multiply Near Base)

A Vedic sutra for multiplying numbers close to a base (10, 100, 1000, etc.). Works by finding how far each number is from the base.

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Anurupyena (Proportion Multiplication)

When numbers are near a convenient working base that is a multiple of a power of 10, use a proportional base to simplify the multiplication.

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Multiply Two Numbers Just Above 100

For numbers a little above 100, use the surplus from 100 to multiply almost instantly.

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