A logarithmic curve passes through the points and and has its vertical asymptote…

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

A logarithmic curve passes through the points

A(1,0)

and

B(36,2)

and has its vertical asymptote along the

y

-axis. (a) Show that the base

a

of the logarithm satisfies

a^{2}=36

and hence find

a

. (b) Write the explicit equation of the curve. (c) Using your equation, find the value of

x

for which the ordinate of the curve is

3

. (d) Determine the interval of

x

for which

x<1

and state the sign (positive or negative) of the corresponding ordinates on that interval.