Suppose that a regression study of quantity supplied as a function of price yielded the following equation: log Q $=5\mathrm{.}2+1\mathrm{.}3$ log P

$($a$)$ What is the elasticity of supply?

$($b$)$ If price increased by $3\%,$ by how much would the quantity supplied increase?

$($c$)$ What price increase would be required to increase the quantity supplied by $10\%?$