tmua 2016 Q16

tmua · Uk · paper1 1 marks Laws of Logarithms Solve a Logarithmic Equation
Given the simultaneous equations
$$\begin{gathered} \log _ { 10 } 2 + \log _ { 10 } ( y - 1 ) = 2 \log _ { 10 } x \\ \log _ { 10 } ( y + 3 - 3 x ) = 0 \end{gathered}$$
the values of $y$ are
A $\frac { 5 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$ B $3 \pm \sqrt { 3 }$ C $7 \pm 3 \sqrt { 3 }$ D 3,9 E 1,13
& C & 16 & C
Given the simultaneous equations

$$\begin{gathered}
\log _ { 10 } 2 + \log _ { 10 } ( y - 1 ) = 2 \log _ { 10 } x \\
\log _ { 10 } ( y + 3 - 3 x ) = 0
\end{gathered}$$

the values of $y$ are

A $\frac { 5 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$
B $3 \pm \sqrt { 3 }$
C $7 \pm 3 \sqrt { 3 }$
D 3,9
E 1,13