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Logarithms
Calculators perform logarithm calculations.
Each page contains a graph and an overview of formulas.
Calculators
logarithm
$$ \begin{aligned} & \log_a x \end{aligned} $$
natural logarithm
$$ \begin{aligned} & \ln x = \log_e x \end{aligned} $$
common logarithm
$$ \begin{aligned} & \log x = \log_{10} x \end{aligned} $$
Formulas
$$ \begin{aligned} & y = \log_a x \ \Longleftrightarrow \ x = a^y \\ \\ \\ & \log x = \log_{10} x \\ \\ & \ln x = \log_e x \\ \\ & e \doteq 2.72 \end{aligned} $$
$$ \begin{aligned} & \log_a x = \frac{\log_b x}{\log_b a} = \frac{\log x}{\log a} = \frac{\ln x}{\ln a} \\ \\ & \log_a x = \frac{1}{\log_x a} \\ \\ & \log_a \left(x \cdot z\right) = \log_a x + \log_a z \\ \\ & \log_a \left(\frac{x}{z}\right) = \log_a x - \log_a z \end{aligned} $$
$$ \begin{aligned} & \log_a x^r = r \cdot \log_a x \\ \\ & \log_a a^r = r \\ \\ & a^{\log_a x} = \log_a a^x = x \end{aligned} $$
$$ \begin{aligned} & \log_a 1 = 0 \\ \\ & \log_a a = 1 \\ \\ \end{aligned} $$
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logarithms
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logarithm
natural logarithm
common logarithm
area and perimeter
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circle
triangle
right-angled triangle
square
rectangle
rhombus
parallelogram
trapezium
pentagon
hexagon
polygon
Pythagorean theorem
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sphere
prism
pyramid
percentage
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linear equation
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arithmetic mean
weighted arithmetic mean
powers and roots
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square
cube
Nth power
square root
cube root
Nth root
trigonometric functions
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sine
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tangent
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unit conversion
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length
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volume
mass
speed
temperature
angles
pressure
power
energy
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electricity consumption
fuel consumption
gas consumption