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}?
-
- - a+b
- - a-b
- - 10^{x+y}
- - 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?
- \log_{10}(a-b)=\log_{10}\left(10^{x-y}\right)
- \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}\left(10^{x-y}\right)
@@ -276,10 +259,10 @@
Recall that this property was covered in .
- - \log_{10}(a-b)
- - \log_{10}(x-y)
- - x-y
- - a-b
+ - \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}(a-b)
+ - \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}(x-y)
+ - \log_{10}\left(\dfrac{a}{b}\right)=x-y
+ - \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.)
- - \log_{10}a=x
- - \log_{x}a=10
- - \log_{10}b=y
- - \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?
-
- - 10^{a+b}
- - \log_{10}a-\log_{10}b
- - \log_{10}a-\log_{10}b
- - 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?
- - \log_{10}(a-b)=10^{a+b}
- - \log_{10}(a-b)=\log_{10}a-\log_{10}b
+ - \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}a+\log_{10}b
+ - \log_{10}\left(\dfrac{a}{b}\right)=10^{x-y}
- \log_{10}\left(\dfrac{a}{b}\right)=\log_{10}a-\log_{10}b
- - \log_{10}\left(\dfrac{a}{b}\right)=10^{x-y}
+ \log_{10}\left(\dfrac{a}{b}\right)=10^{x+y}