1. Warm up honors algebra 2 3/7/19
Find the inverse function:
1. 𝑦=2𝑥 𝑦=3 ln 𝑥+1
2. 𝑓 𝑥 =2 𝑥 𝑓 𝑥 =4 5 𝑥

2. Find the inverse function
𝑓 𝑥 = 𝑥
𝑥= 𝑦
𝑥 5 = 𝑦
𝑙𝑜𝑔 𝑥 5 =𝑦= 𝑓 −1 (𝑥)

3. Which equations are true for all values of x? Select all that apply.
B) ( 3 𝑥 ) 2 = (3 2 ) 𝑥
C) 27 𝑥 = ( 3 𝑥 ) 3
D) 3 𝑥+2 =9( 3 𝑥 )
E) 9 𝑥+2 = 3 2𝑥+4

4. Same exponential bases
What happens if exponential terms have the same bases?
2 (2𝑥) = 2 (𝑥+4)
2𝑥=𝑥+4
𝑥=4

5. Solve 8 𝑥 = 2 𝑥+6 8 𝑥  (2 3 ) 𝑥  2 3𝑥 2 3𝑥 = 2 𝑥+6 3𝑥=𝑥+6 2𝑥=6 𝑥=3
Rewrite each side so that they have the same base
8 𝑥  (2 3 ) 𝑥  2 3𝑥
2 3𝑥 = 2 𝑥+6
3𝑥=𝑥+6
2𝑥=6
𝑥=3

6. 16 𝑥  (4 2 ) 𝑥  4 2𝑥 4 4𝑥+1 =4 2𝑥 4𝑥+1=2𝑥 1=−2𝑥 𝑥=− 1 2
Solve 4 4𝑥+1 = 16 𝑥
16 𝑥  (4 2 ) 𝑥  4 2𝑥 4 4𝑥+1 =4 2𝑥 4𝑥+1=2𝑥 1=−2𝑥 𝑥=− 1 2

7. 144 2𝑥  ( 12 2 ) 2𝑥  12 4𝑥 12 4𝑥 = 12 6𝑥−1 4𝑥=6𝑥−1 −2𝑥=−1 𝑥= 1 2
Solve 𝑥 = 12 6𝑥−1
144 2𝑥  ( 12 2 ) 2𝑥  12 4𝑥
12 4𝑥 = 12 6𝑥−1
4𝑥=6𝑥−1
−2𝑥=−1
𝑥= 1 2

8. 25 5𝑥  (5 2 ) 5𝑥  5 10𝑥 5 𝑥+3 = 5 10𝑥 𝑥+3=10𝑥 3=9𝑥 𝑥=1/3
Solve 5 𝑥+3 = 25 5𝑥
25 5𝑥  (5 2 ) 5𝑥  5 10𝑥 5 𝑥+3 = 5 10𝑥 𝑥+3=10𝑥 3=9𝑥 𝑥=1/3

9. Solve 36 −3𝑥 = 6 2𝑥−1 36 −3𝑥  (6 2 ) −3𝑥  6 −6𝑥 6 −6𝑥 = 6 2𝑥−1
36 −3𝑥  (6 2 ) −3𝑥  6 −6𝑥
6 −6𝑥 = 6 2𝑥−1
−6𝑥=2𝑥−1
−8𝑥=−1
𝑥=1/8

10. Solve −49 −𝑥 = 7 3𝑥−1
−49 −𝑥  −( 7 2 ) −𝑥  −( 7 −2𝑥 ) −(7) −2𝑥 = 7 3𝑥−1 − −2𝑥 =3𝑥−1 2𝑥=3𝑥−1 −𝑥=−1 𝑥=1

11. A bank pays depositors a 2% interest rate compounded semi-annually
A bank pays depositors a 2% interest rate compounded semi-annually. Let P represent an initial deposit, and t represent the number of years that the deposit is in the bank. The expression 𝑃 𝑡 can be used to determine the account balance after t years. Which expression accurately reflects the annual interest rate?
A) 𝑃 𝑡
B) 𝑃 𝑡
C) 𝑃 𝑡
D) 𝑃 𝑡

12. Solve for n
𝑛 =4.305
𝑛 =0.316
𝑛 =14,521
𝑛 =
log =𝑛
log =𝑛
log 14,521 =𝑛
log =𝑛
𝑛=.634
𝑛=−.5003
𝑛=4.162
𝑛=2.684