7.163. Knowing that $\lg 2=a$ and $\log _{2} 7=b$, find $\lg 56$.
## Solution.

$\lg 56=\lg (7 \cdot 8)=\lg 7+\lg 8=\lg 7+3 \lg 2=\frac{\log _{2} 7}{\log _{2} 10}+3 \lg 2=\log _{2} 7 \cdot \lg 2+3 \lg 2=$

$=a b+3 a=a(b+3)$.

Answer: $a(b+3)$.