Question

Find a so that the graph of f(x)=loga(x) contains the point (1/7, -14). Give your answer to 2 decimal places.

a=

Answer 1

we are givenan x and a y value from the point, and are asked to find "a" which is just the base

Answer 2

y = loga(x) , to solve for "a", change of base it maybe

y = ln(x)/ln(a) ; multiply thru by ln(a), and divide out the y

ln(a) = ln(x)/y ; take the "e" of each side

e^(ln(a)) = e^(ln(x)/y) ; simplify

a = e^(ln(x)/y)

Answer 3

y=log_a(x)=lnx/lna
-14=ln(1/7)/lna

-14lna=ln(1/7)

lna=-1/14*ln(1/7)
e^ e^

a=e^{-1/14*ln(1/7)}

a=e^{ln(1/7)^(-1/14)}

a=(1/7)^(-1/14)

is what i get but i'm just a beginner so i could be wrong

Answer 4

yes! that was right (: thank you guys.

Answer 5

omg i can do math thats so weird

Answer 6

yours looks to be good :) with the numbers added in it appears to adjust more, but yep :)

Answer 7

im sorry i think you guys like to call it maths

Answer 8

is tht right?
lol

Answer 9

its like a cat; it doesnt matter what you call it, it wont come until its ready :)