1. Warmup
Solve 2x – 4 = 14. Round to the nearest ten-thousandth. Show all logarithmic work.

2. 6-8 Natural Logarithms
Evaluate expressions with natural base and natural logarithms.
Solve exponential equations and inequalities using natural logarithms.

3. 𝑒 1 = ? 𝐴 𝐶𝑂𝑁𝑆𝑇𝐴𝑁𝑇!

4. Write an equivalent exponential or logarithmic function
20. ln 0.25 =𝑥

5. Write an equivalent exponential or logarithmic function
𝑒 𝑥−3 =2

6. Write as a single logarithm
Write as a single logarithm. End result should have no operations and no powers.
ln 𝑙𝑛 2

7. Solve. Round to the nearest ten-thousandth.
37.
(isolate the exponential part, then put in logarithmic form to get x by itself)

8. Solve each inequality. Round to the nearest ten-thousandth.
40. 𝑒 𝑥 ≥42.1

9. Recall that if interest is compounded n times a year, we use 𝐴=𝑃 (1+ 𝑟 𝑛 ) 𝑛𝑡
If the interest is compounded every second of every day, or continuously, we use:
Exponential: 𝐴=𝑃 𝑒 𝑟𝑡 Logarithmic: 𝑙𝑛 𝐴 𝑃 =𝑟𝑡

10. 51. Use the logarithmic and exponential formulas for continuous interest
You are on your own for a, b.
c) Double money in 9 years, what rate?
d) 10,000 after 12 yrs at 4.75%, what is initial deposit?