\( \begin{array}{l}\text { xample:- Solve the following system of equations by L } \\ \text { Decomposition } \\ \text { decomposition } \\ x_{1}+5 x_{2}+12 x_{3}=47 \\ x_{1}+2 x_{2}+3 x_{3}=14 \\ 2 x_{1}+4 x_{2}+3 x_{3}=19\end{array} \)

\( \begin{array}{ll}\text { a) }(-5)^{4} \cdot(-2)^{4} & \text { b) }(-4)^{4} \cdot(-5)^{4} \\ \text { c) }(-18)^{3}:(-6)^{3} & \text { d) }(+35)^{3}:(-7)^{3} \\ \text { e) }\left[(-5)^{3}\right]^{2}:(-5)^{5} & \text { f) }\left[(+8)^{4}\right]^{3}:(-8)^{10}\end{array} \)

6) \( (x-8)(x-3)(x-5)=(x-5)(x-3)(x-6) \)

a) \( \frac{12 a b}{4 a}= \)

4. Find the value of \( k \) so that the equation \( k x^{2}+k x+1=-4 x^{2}-x \) have equal roots. 5. For what values of \( m \) will the equation \( x^{2}-2(5+2 m) x+3(7+10 m)=0 \) have equal roots? 6. If the roots of the equation \( \left(a^{2}+b^{2}\right) x^{2}-2(a c+b c) x+\left(c^{2}+c^{2}\right)=0 \) are cqual, then prove the \( a \) c \( c \)

5) Qual a expressão cujo desenvolvimento logarítmico é dado abaixo ( \( a, b \), c são reais positivos)? a) \( \log _{2} a+\log _{2} b-\log _{2} c \) b) \( \frac{1}{3} \log a-\frac{1}{2} \log c-\frac{3}{2} \log b \) c) \( 2+\frac{1}{3} \log _{2} a+\frac{1}{6} \log _{2} b-\log _{2} c \) d) \( \frac{1}{2} \log (a-b)+\log a-\log (a+b) \)