Mathematician's Name: ____________________________ Algebra II January_______ 2017 Log/Exp. Equations HW 1. Expand the following logarithms: a. log !
!!
!!
b. ln
!! !
!!
2. Condense the following into a single logarithm: a.
!
!
ln 𝑦 + ln 𝑥 − 3 ln 𝑦 b. 4[log 𝑥 + 1 + log 𝑦 − log 𝑏] 3. Simplify the following until you have x as either a single exponential or logarithmic expression (for example, 𝑥 = log ! 7 or 𝑥 = 𝑒 ! ). If starred, you should be able to solve for an integer answer. a. 5 + 3 ln 𝑥 = 17 e. 2 ln 5𝑥 + 1 = 10 b. 𝑒 !! = 8 f.
c.
g. ∗∗ 2 5 ! = 10 ∗∗ **2 log ! 𝑥 = 4 ∗∗ d. **1 − 4 2 ! = −31 ∗∗ 3𝑒 !! = 6 h. 3 log ! 2𝑥 = 9
Mathematician's Name: ____________________________ Algebra II January_______ 2017 Log/Exp. Equations HW 4. Evaluate: a. log ! 9 = c.
log 100 = b. log ! 1 = d. ln 𝑒 ! = e. log ! 16 = f.
5. Solve for x: a. 3 ! = 9 e. 4!! = 8 b. 4 !!! = 64 f.
c.
5!!!! = 1 d. 16 ! = 64 6. Favorite color? 𝑥 !/! = 4 g. 8!! = 2!!!! h.
2𝑥
!
= 64 log !
!
!"
=