Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our 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).

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.