Answer:
m = 5 and c = -2
Step-by-step explanation:
[tex]let \: y = \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} \\ be \: equation \: 1[/tex]
Now
[tex]y = \sqrt{5} ( \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} ) \\ y = \sqrt{100} \times {10}^{ - 3} \times {10}^{5x} \\ y = 10 \times {10}^{ - 3} \times {10}^{5x} [/tex]
[tex]using \: rules \: of \: indices \: we \: get \\ y = {10}^{1 - 3 + 5x} \\ y = {10}^{ - 2 + 5x} \\ [/tex]
[tex]now \: take \: log \: of \: both \: sides \: and \: use \: laws \: of \: logarithm \\ we \: get \\ [/tex]
[tex] log(y) = log( {10}^{ - 2 + 5x} ) \\ log(y) = ( - 2 + 5x) log(10) \\ log(y) = - 2 + 5x \\ log(y) - 5x = - 2 \\ \\ comparing \: this \: to \: \\ log(y) - mx = c \\ \\ we \: get \: m \: = 5 \: and \: c = - 2[/tex]
