Exponentials and Logarithms (C7) Flashcards
What is another way of writing a = b^c
c = log (little b)a
Where do exponentials cross the y axis and why?
They cross the y axis at y = 1, because a^0 from y = a^x is always 1.
What is the relationship between x and y, with y = a^x for a>1?
As x increases, y increases as a>1.
Also,as x decreases, y decreases at a smaller and smaller rate.
What is the minimum point y can reach on an exponential graph?
It will get infinitely close to 0, but never reach it.
What is the relationship between x and y, with y = a^x for a is bigger than 0 but less than 1?
As x increases, y decreases as a is bigger than 0 but smaller than 1.
As x increases, y decreases at a smaller and smaller rate.
What is the value of a which means the gradient of y = a^x is identical to the value of a^x?
It is the irrational number e, around 2.7183.
What is the gradient of y = e^kx, where k is a constant?
Gradient = ke^kx
What is the gradient of y = Ae^kx, where A and k are both constants?
Gradient = Ake^kx
What do you get from the calculation:
log a x + log a y ?
log a (x*y)
What is another way of writing k*log a x?
log a x^k
What is a way of calculating a log with a non - 10 base?
log a x = (log b x)/(log b a) with b as 10
What is another way of writing
log(30) - log(10)
Log30-log10
Log(30/10)
Log(3)
