How to find the rule of this logarithm graph, (2nd question)?

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1 Answer
Apr 15, 2018

The vertical asymptote will always be the corresponding value of #b#.

Thus we can we already say the graph is

#y = alog_e(x -1) + c#

We may also change the base #e# to #ln#.

#y = aln(x - 1) +c#

We now set up a system of equations

#{(10 = aln(2) + c), (12 = aln(4) + c):}#

Subtract the second equation from the first:

#-2 = aln(2) - aln(4)#

#-2= a(ln(2) - ln(4))#

#-2 = aln(1/2)#

#-2/ln(1/2) = a#

I will leave solving for #c# up to you.

Hopefully this helps!