waengg
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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]

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.