Aim: How do we solve exponential equations using common or natural logarithms? Do Now: 1. Solve for x: 3 x = Solve for x: 4 x = 8 3. Solve for x: 3 x = 5 Homework: p.343 # 4,6,8,10,12,14 p.340 d & f p.339 # 44,46

We can solve 3 x = 27 and 4 x = 8 after writing each side of the equation as a power to the same bases. But we can not write 3 and 5 into the base, therefore, we need to use different method to solve 3 x = 5 log 3 x = log 5 Write log on both sides x log 3 = log 5 Use power rule to rewrite left side Solve for x

If 9 x = 14, find x to the nearest tenth log 9 x = log 14 Write log on both sides Use power rule to rewrite left side x log 9 = log 14 Solve the equation for x Solve for x to the nearest tenth: x = x = 500 log 12 1+x = log 500 (1 + x) log 12 = log 500 x  1.5

1. Find x to the nearest tenth:15 x = Find x to the nearest tenth: log 4 3 = x 3. Solve for x to the nearest tenth: 5 x = 0.36 x  2.1 x  0.8 x  –0.6

Solve for x to the nearest hundredth: 1. 5(7) x = (2 x ) = 815 Both sides divided by 5 Write ln on both sides ln 7 x = ln 330 Use power rule to rewrite left side x ln 7 = ln 330 Solve for x x  x = 122 x  2.14

Find the positive value of x: Multiply log on both sides Use power rule Divide both sides by log 6 simplify Solve for x: x = 0, x = 3

The amount of money, A, in the bank is determined by P is principal, r is interest rate, n is number of times each year that interest is compounded, t is number of years John invested $10,000 in the bank with annual interest rate 6%, compounded semiannually 1. What will be the amount in his account after 5 years? 2. How long must $10,000 be left in the account in order for the value of the account to be 13,500? 3. How long will the original amount be doubled?