Download MR12 Lsn 55

Aim: How do we solve exponential equations
using common or natural logarithms?
Do Now: 1. Solve for x: 3x = 27
2. Solve for x: 4x = 8
3. Solve for x: 3x = 5
Homework:
p.343 # 4,6,8,10,12,14 p.340 d & f p.339 # 44,46
We can solve 3x = 27 and 4x = 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 3x = 5
log 3x = log 5
x log 3 = log 5
log 5
x
 1.465
log 3
Write log on both sides
Use power rule to rewrite left side
Solve for x
If 9x = 14, find x to the nearest tenth
log 9x = log 14
Write log on both sides
Use power rule to rewrite left side
x log 9 = log 14
log 14
x
 1.2
log 9
Solve the equation for x
Solve for x to the nearest tenth: 12 • 12x = 500
log 121+x = log 500
121+x = 500
(1 + x) log 12 = log 500
log 500
1 x 
log 12
log 500
x
1
log 12
x  1.5
1. Find x to the nearest tenth:15x = 295
x  2.1
2. Find x to the nearest tenth: log4 3 = x
x  0.8
3. Solve for x to the nearest tenth: 5x = 0.36
x  –0.6
Solve for x to the nearest hundredth:
1. 5(7)x = 1650
Both sides divided by 5
1650
7 
 330
5
Write ln on both sides
ln 7x = ln 330
x
Use power rule to rewrite left side
Solve for x
2. 7(2x) = 815
3. 12 + 9x = 122
x ln 7 = ln 330
ln 330
x
 2.98
ln 7
x  6.86
x  2.14
Find the positive value of x:
Multiply log on both sides
Use power rule
6
x 2 3 x
log 6
x 2 3 x
1
 log 1
( x  3x) log 6  log 1
2
log 6 log 1
Divide both sides by log 6 ( x  3x)

log 6 log 6
log 1
0
2

0
simplify
x  3x  0
log 6 log 6
2
Solve for x:
x( x  3)  0,
x = 0, x = 3
The amount of money, A, in the bank is determined by
r nt
A  p (1  )
n
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?