4.7.3 Practice: Exponential and Logarithmic Functions
Answer the following questions using what you've learned from this unit. Write your responses in
the space provided.
1. Check all correct answers (there may be more than one). (2 points)
In the expression ab ,
Check → A. The value b is an exponent.
_____B. The value a tells you how many times to multiply b by itself.
_____C. The value a must be > 1.
Check -->D. The value b tells you how many times to multiply a by itself.
_____E. The value b must be an integer.
2. Simplify the expression below. Write your answer with only positive exponents. (2 points)
=
(a^2b^2c/a^5c^2)(a^3b/c^4)
Remove parentheses: a^2b^2c/a^5c^2* a^3b/c^4
Multiply to get a^3b/c64* b^2a^3c
Multiple fractions to get: b^2a63b/a^3cc^4
Cancel the common factor a^3 to get: b^b/cc^4
b^2b=b^3
b^3/c^4c
cc^4=c^5
Final answer:b^3/c^5
, 3. Combine into a single logarithm. (2 points)
=
3log10(x+y)+2log10(x-y)-loh10(x^2+y^2)
log10(x+y)^3+log10(x-y)^2-log10(x^2+y^2)
log10((x+y)^3)*((x-y)^2))-log10(x^2+y^2)
log10((((x+3)^3)*((x-y)^2))))/(x^2+y^2))
4. Use rules of logarithms to expand. (2 points)
=
log10((x+3)^2)-log10((x-2)(x^2)^4)
2log10(x+3)-(log10(x-2)+4log10(x^2+5))
2log10(x+3)-log10(x-2)-4log10(x^2+5)
5. Rewrite as an exponential equation. (2 points)
x=-y+e^5
6. Rewrite as a logarithmic equation. (2 points)
log2(a-b)=4
7. Evaluate each expression. (4 points)
a.
rewrite 32 into power base form.
Answer the following questions using what you've learned from this unit. Write your responses in
the space provided.
1. Check all correct answers (there may be more than one). (2 points)
In the expression ab ,
Check → A. The value b is an exponent.
_____B. The value a tells you how many times to multiply b by itself.
_____C. The value a must be > 1.
Check -->D. The value b tells you how many times to multiply a by itself.
_____E. The value b must be an integer.
2. Simplify the expression below. Write your answer with only positive exponents. (2 points)
=
(a^2b^2c/a^5c^2)(a^3b/c^4)
Remove parentheses: a^2b^2c/a^5c^2* a^3b/c^4
Multiply to get a^3b/c64* b^2a^3c
Multiple fractions to get: b^2a63b/a^3cc^4
Cancel the common factor a^3 to get: b^b/cc^4
b^2b=b^3
b^3/c^4c
cc^4=c^5
Final answer:b^3/c^5
, 3. Combine into a single logarithm. (2 points)
=
3log10(x+y)+2log10(x-y)-loh10(x^2+y^2)
log10(x+y)^3+log10(x-y)^2-log10(x^2+y^2)
log10((x+y)^3)*((x-y)^2))-log10(x^2+y^2)
log10((((x+3)^3)*((x-y)^2))))/(x^2+y^2))
4. Use rules of logarithms to expand. (2 points)
=
log10((x+3)^2)-log10((x-2)(x^2)^4)
2log10(x+3)-(log10(x-2)+4log10(x^2+5))
2log10(x+3)-log10(x-2)-4log10(x^2+5)
5. Rewrite as an exponential equation. (2 points)
x=-y+e^5
6. Rewrite as a logarithmic equation. (2 points)
log2(a-b)=4
7. Evaluate each expression. (4 points)
a.
rewrite 32 into power base form.
