Question

by letting P=46^(-y) in the equation 4^(-2y+1)-3x4^(-y)-10=0
(a)write the above equation in terms of p
(b)hence find the possible values of p

Answer 1

@Hero

Answer 2

@bibby

Answer 3

@zscdragon hello???

Answer 4

\[ \large
4^{-2y+1}-3*4^{-y}-10=0 \\ \large
4^{-2y}*4 - 3*4^{-y}-10=0 \\ \large
4(4^{-y})^2 - 3(4)^{-y} - 10 = 0 ~~~---- (1) \\ \large
\text{ } \\ \large
p = (46)^{-y} \\ \large
\log(p) = -y * \log(46) \\ \large
-y = \log(p) / \log(46) ~~~---- (2) \\ \large
\text{ } \\ \large
\text{For a): put (2) in (1) } \\ \large
\]

Answer 5

For b) it is easier to solve (1) and then find p.
\[ \large
4(4^{-y})^2 - 3(4)^{-y} - 10 = 0 ~~~---- (1) \\ \large
\text{ } \\ \large
\text{Let } t = 4^{-y} \\ \large
4t^2 - 3t - 10 = 0 \\ \large
4t^2 - 8t + 5t - 10 = 0 \\ \large
4t(t-2) + 5(t-2) = 0 \\ \large
(4t+5)(t-2) = 0 \\ \large
t = 2, -\frac 54 \\ \large
4^{-y} = 2, -\frac 54 \\ \large
\text{Take log to the base 2:} \\ \large
-y*2 = 1; -y = \frac 12; ~~p = (46)^{-y} = 46^{1/2} = \sqrt{46}.
\]

Follow a similar procedure for t = -5/4 and find p.

Answer 6

t = -5/4 can be ignored as an extraneous solution because 4^(-y) cannot be a negative number for any real value of y and so 4^(-y) cannot be -5/4.

Answer 7

thanks