Solve the system by using any method.
-$\log x + 4 \log y = 11$
$3 \log x - \log y = 7$
A) $\{ ( 0.001,0.01 ) \}$
B) $\{ ( 1,000,100 ) \}$
C) $\{ ( - 3 , - 2 \}$
D) $\{ ( 3,2 ) \}$

Question

Quizplus · Accepted Answer

The system of logarithmic equations can be solved by first using the properties of logarithms to simplify each equation. The first equation can be rewritten as $\log x + \log y^4 = 11$ or $\log(xy^4) = 11$, which implies $xy^4 = 10^{11}$. The second equation can be rewritten as $\log x^3 - \log y = 7$ or $\log \frac{x^3}{y} = 7$, which implies $\frac{x^3}{y} = 10^7$. Solving these equations simultaneously, we find $x = 1000$ and $y = 100$, which corresponds to choice B.

Solve the System by Using Any Method log⁡x+4log⁡y=11\log x + 4 \log y = 11logx+4logy=11

Solve the System by Using Any Method $\log x + 4 \log y = 11$