waengg
Answered

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given that y/√5 = √20 ×10^-3×10^5x. and lgy- mx = c for x>0 and y>0, find the values of m and c​

Sagot :

etanauriel

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]

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