Asked by Jessie
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!
Can you please explain how to answer this question? Thanks!
Answers
Answered by
Reiny
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(x-4)+3
intersection:
2log(x-4) + 3 = logx
log(x-4)^2 - logx = -3
log ( (x-4)^2 /x ) = -3
(x-4)^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(x-4) , x-4> 0 , so our 2nd answer is rejected
x = appr 4.06
if x = 4.06, then y = log 4.06 = appr .61
so you have y= logx
and y = 2log(x-4)+3
intersection:
2log(x-4) + 3 = logx
log(x-4)^2 - logx = -3
log ( (x-4)^2 /x ) = -3
(x-4)^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(x-4) , x-4> 0 , so our 2nd answer is rejected
x = appr 4.06
if x = 4.06, then y = log 4.06 = appr .61
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