Mathematics Trig Graphs

Question

The diagram shows part of the graph of y=logb(x+a)

determine the the values of a and b

(3,0)

(7,1)

Answer 1

(3,0) means x=3 and y=0

So, 0 = logb(3+a)

then

B^0 = B^(logb(3+a))

1 = 3+a

a=-2

The function is now y = Logb(x-2)

This holds for any base B

Now it;s time to find the PARTICULAR base B....

(7,1) means x=7 and y=1

1 = logB(7-2)

1 = logB(5)

B^1 = B^(logB(5))

B = 5

so the final function is

y = Log5(x-2)