Exponentials and logarithms

Question 1

loga b meaning

Answer 1

a to the power of what = b

Question 2

log combinations

Answer 2

log a + log b = logab
log a - log b = log a/b
x log a = log a^x

Question 3

ln (x)

Answer 3

same as saying log e (x)

Question 4

differentiation of x

Answer 4

dy/ dx of e^2x = 2e^2x
x can be anything else e.g dy/dt of 4e^3t = 12e^3t

Question 5

linearising exponentials

Answer 5

y = ab^x
log y = log a + x log b
as y = mx + c
so draw a graph of log y against x
log a is y intercept and log b is gradient
for a do intercept^10
for b do gradient ^ 10

Question 6

linearising polynomials

Answer 6

y = ax^b
log y = log a + t log x
y = mx + c so
draw graph of log y against log x
log a is y intercept and b is gradient
a = 10^intercept and b is m