diff --git a/source/precalculus/source/05-EL/05.ptx b/source/precalculus/source/05-EL/05.ptx index e34f0478a..18bd14b4b 100644 --- a/source/precalculus/source/05-EL/05.ptx +++ b/source/precalculus/source/05-EL/05.ptx @@ -236,25 +236,8 @@

- Let a=10^x and b=10^y. How could you rewrite the left side of the equation \dfrac{10^x}{10^y}? -

    -
  1. a+b
  2. -
  3. a-b
  4. -
  5. 10^{x+y}
  6. -
  7. a \cdot b
-

-
- -

- B -

-
-
- - - -

- Use the one-to-one property of logarithms to apply the logarithm to both sides of the rewritten equation from part (a). What is that equation? + If we let a=10^x and b=10^y and apply a logarithm + to both sides of the equation, what would be the result?

  1. \log_{10}(a-b)=\log_{10}\left(10^{x-y}\right)
  2. \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}\left(10^{x-y}\right)
  3. @@ -276,10 +259,10 @@ Recall that this property was covered in .
      -
    1. \log_{10}(a-b)
    2. -
    3. \log_{10}(x-y)
    4. -
    5. x-y
    6. -
    7. a-b
    +
  4. \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}(a-b)
  5. +
  6. \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}(x-y)
  7. +
  8. \log_{10}\left(\dfrac{a}{b}\right)=x-y
  9. +
  10. \log_{10}\left(\dfrac{a}{b}\right)=a-b

@@ -292,12 +275,12 @@

- Recall in part (a), we defined 10^x=a and 10^y=b. What would these look like in logarithmic form? + Recall in part (a), we defined 10^x=a and 10^y=b. What would these look like in logarithmic form? (Choose two.)

    -
  1. \log_{10}a=x
  2. -
  3. \log_{x}a=10
  4. -
  5. \log_{10}b=y
  6. -
  7. \log_{y}b=10
+
  • x=\log_{10}a
  • +
  • x=\log_{a}10
  • +
  • y=\log_{10}b
  • +
  • y=\log_{b}10
  • @@ -306,32 +289,14 @@

    - - - -

    - Using your solutions in part (d), how can we rewrite the right side of the equation? -

      -
    1. 10^{a+b}
    2. -
    3. \log_{10}a-\log_{10}b
    4. -
    5. \log_{10}a-\log_{10}b
    6. -
    7. 10^{x-y}
    -

    -
    - -

    - B -

    -
    -
    -

    Combining parts (a) and (d), which equation represents \dfrac{10^x}{10^y}=10^{x-y} in terms of logarithms? +

    Combining these results, which equation represents \dfrac{10^x}{10^y}=10^{x-y} in terms of logarithms?

      -
    1. \log_{10}(a-b)=10^{a+b}
    2. -
    3. \log_{10}(a-b)=\log_{10}a-\log_{10}b
    4. +
    5. \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}a+\log_{10}b
    6. +
    7. \log_{10}\left(\dfrac{a}{b}\right)=10^{x-y}
    8. \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}a-\log_{10}b
    9. -
    10. \log_{10}\left(\dfrac{a}{b}\right)=10^{x-y}
    +
  • \log_{10}\left(\dfrac{a}{b}\right)=10^{x+y}