Question

The variables x and y satisfy the equation (x)^ny=C, where n and C are constants. When x=1.10, y=5.20, and when x=3.20, y=1.05. (i) Find the values of n and C.

Answer 1

\[x ^{n}y=C\]

Answer 2

@Michele_Laino

Answer 3

if we substitute your data, we get two different conditions, namely:
\[\Large \begin{gathered}
{\left( {1.1} \right)^n} \cdot 5.2 = C \hfill \\
\hfill \\
{\left( {3.2} \right)^n} \cdot 1.05 = C \hfill \\
\end{gathered} \]
those equation are an algebraic system, which can be solved for n and C

Answer 4

equations*

Answer 5

not being able to solve -_-

Answer 6

if I use the elimination method, I can write this:
\[\Large {\left( {1.1} \right)^n} \cdot 5.2 = {\left( {3.2} \right)^n} \cdot 1.05\]

Answer 7

yesss

Answer 8

now, I divide both sides of that equation by (1.1)^n, so I get:
\[\Large 5.2 = {\left( {\frac{{3.2}}{{1.1}}} \right)^n} \cdot 1.05\]

Answer 9

then I divide both sides again by 1.05, so I can write this:
\[\Large \frac{{5.2}}{{1.05}} = {\left( {\frac{{3.2}}{{1.1}}} \right)^n}\]

Answer 10

okay

Answer 11

we got an exponential equation, which can be solved using logarithms

Answer 12

not getting the right answer

Answer 13

why?

Answer 14

i dont know.. can you continue further ?

Answer 15

ok!

Answer 16

if we take the logarithm in base 10, of both sides, we get:
\[\Large \begin{gathered}
n \cdot {\log _{10}}\left( {\frac{{3.2}}{{1.1}}} \right) = {\log _{10}}\left( {\frac{{5.2}}{{1.05}}} \right) \hfill \\
\hfill \\
n = \frac{{{{\log }_{10}}\left( {\frac{{5.2}}{{1.05}}} \right)}}{{{{\log }_{10}}\left( {\frac{{3.2}}{{1.1}}} \right)}} \hfill \\
\end{gathered} \]

Answer 17

what do you get?

Answer 18

finally got the answer.. thank you very much

Answer 19

thanks! :)