Rewbie5478 Rewbie5478
  • 21-05-2020
  • Mathematics
contestada

Consider the equation 14*10^0.5w=100

Solve the equation for w. Express the solution as a logarithm in base-10

Respuesta :

lisboa lisboa
  • 21-05-2020

Step-by-step explanation:

14*10^0.5w=100

[tex]14*10^{0.5w}=100[/tex]

Solve the equation for w

divide by 14 on both sides

[tex]10^{0.5w}=\frac{100}{14}[/tex]

Convert exponential form into log form

base is 10 so we convert into log form

log (a)= x  then a=10^x

[tex]10^{0.5w}=\frac{100}{14}[/tex]

[tex]0.5w = log(\frac{100}{14} )\\0.5w = log(\frac{50}{7} )\\\\[/tex]

divide both sides by 0.5

[tex]0.5w = log(\frac{50}{7} )\\\\\\w= 2 log(\frac{50}{7} )[/tex]

Answer:

[tex]w= 2 log(\frac{50}{7} )[/tex]

Answer Link

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