Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

If log_10(x) = 3 + log_10(y), then find x/y

Sagot :

mhanifa

Answer:

  •  1000

Step-by-step explanation:

  • [tex]log_{10}x = 3 + log_{10}y[/tex]
  • [tex]log_{10}x - log_{10}y = 3[/tex]
  • [tex]log_{10}(x/y) = 3[/tex]
  • [tex]x/y = 10^3[/tex]
  • [tex]x/y = 1000[/tex]

sqdancefan

Answer:

  x/y = 10^3 = 1000

Step-by-step explanation:

The rules of logarithms tell you ...

  log(x/y) = log(x) -log(y)

__

Here, we have ...

  log(x/y) = log(x) -log(y)

  = (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)

Taking the antilog, we get ...

  log(x/y) = 3

  x/y = 10^3 = 1000

_____

Additional comment

The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).

In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.