e graph of fx can also be described by the equation gx a log

e graph of f(x) can also be described by the equation g(x) a log, x. Find the value of a

15) f(x) = log8(x) ; g(x) = alog2(x)

f(x) = logx/log8 = logx/3log2 = (1/3)log2(x)

So, a = 1/3

17) g(x) = alog2(x) +k

(1/4 , -9) and (16, -6)

Plug each point and form equations:

(1/4 , -9)

-9 = alog2(1/4) +k

-9 =a log(2^-2)/log2 +k

-9 = -2a +k ----(1)

(16, -6)

-6 = alog2(16) +k

-6 = alog(2^4)/log2 +k

-6 = a*4 +k ----(2)

solve 1 and 2 to get a and k : -9 +6 = -2a -4a

-6a= -3 ; a = 1/2

-6 = (1/2)*4 +k ; k = -6 -2 = -8

So, g(x) = (1/2)log2(x) - 8