Equation of a straight line - y-intercept and gradient

In the general equation for the straight line y = mx + c
c is the point where the line crosses the y-axis (the "y-intercept"), and m is the steepness of that line (gradient, or "rise/run")

Logarithms and Exponentials

log_bn = x Û n = b^x
log expression exponential expression

eg. if log₆44 = 0.333 then 4 = 64^0.333

Remember you will mostly work with log₁₀
which is the log button on your calculator.

Law 1 log_b mn = log_b m + log_b n

Law 2 log_b (m/n) = log_b m - log_b n

Law 3 log_b 1 = 0 (b ¹ 0)

Law 4 -log_b m = log_b (1/m) (b ¹ 0)

Law 5 log_b m^a = alog_b m

Here b is the base, n is the number you are taking the log of, y is the power.

- check this on your calculator.

log₁₀n = x Û n = 10^x

The Laws of Indices

Law 1 b^x x b^y = b^x+y

Law 2 b^x x b^y = b^x+y

Law 3 b⁰ = 1

Law 4 b^-x = 1/b^x

Law 5 (b^x)^y = b^xy

Law 6 (ab)^x = a^x b^y

Law 7 b^1/x = ^xÖ b

y = e^kx e and k are both constants,
e is Euler's constant 2.718281... and is a special logarithmic base.

Law 1 e^x x e^y = e^x+y

Law 2 e^x x e^y = e^x+y

Law 3 e⁰ = 1

Law 4 e^-x = 1/e^x

Law 5 (e^x)^y = e^xy

Law 6 (ae)^x = a^x e^y

Law 7 e^1/x = ^xÖ e

ln is the natural logarithmic function and can be considered then as log_e

Logarithmic laws

Law 1 ln mn = ln m + ln n

Law 2 ln (m/n) = ln m - ln n

Law 3 ln 1 = 0

Law 4 - ln m = ln (1/m)

Law 5 ln m^a = a ln m