Question

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

Answer 1

Answer:

  x/y = 10^3 = 1000

Step-by-step explanation:

The rules of logarithms tell you ...

  log(x/y) = log(x) -log(y)

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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

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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).

Answer 2

Answer:

•  1000

Step-by-step explanation:

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