Advanced Functions/ Precalculus Log
posted by Jessie on .
If (x, y) is on the graph f(x) = log(base10)x, state the coordinates (in terms of x and y) that would be on the graph of f(x) = 2log(base10)(x  4) + 3?
Can you please explain how to answer this question? Thanks!

remember if the base of the log is 10, we don't have to write the base.
so you have y= logx
and y = 2log(x4)+3
intersection:
2log(x4) + 3 = logx
log(x4)^2  logx = 3
log ( (x4)^2 /x ) = 3
(x4)^2 /x = 10^3
x^2  8x + 16 = (1/1000)x
1000x^2  8001x + 16000=0
using the formula
x = (8001 ± 126.5)/2000
= 4.06 or 3.94
but in 2log(x4) , x4> 0 , so our 2nd answer is rejected
x = appr 4.06
if x = 4.06, then y = log 4.06 = appr .61