Section 4.4
Notes
CAT
Exponential and Logarithmic Equations
I
Common Bases – make the bases the same. Set the exponents equal.
76x = 72x-20
64
x+1
=4
4
9x = 3
x-1
81
=3
8x 
x+2
2x-1
9
1
64
= 27
9-x = 27
x+4
1
23 x1   
8
x
II Different Bases – get the exponent term alone. Take the log/ln of both sides.
4x = 80
ex = 8
43x + 2 = 3
4ex + 3 = 23
2(7)x - 4 = 8
6e2x = 4
3x+5 = 15
32x-1 = 7x+1
Solving Logarithmic Equations
I One log – Get the log alone, if necessary. Change to exponential form. Check for extraneous
roots!
Log3x = 5
log2x = 3
log 4x = -1
ln x = 3
4ln (3x) = 8
log2(4x – 4) = 5
2log(2x + 5) = 4
log6(4x + 12) = 2
II One log each side – Set the arguments equal to each other.
Log3(x + 2) = log3(3x)
log6(3y – 5) = log6(2y + 3)
log2(10x) = log2(3x + 14)
III Extra logs – Condense to a single log. Change to exponential form. Check for extraneous
roots!
log x – log 4 = 3
log4 5 + log4 x = log4 60
logx + log(x – 3) = 1
log3d + log33 = 3
log4(n + 1) – log4(n – 2) = 1
ln(x-3)=ln(7x–23)–ln(x+1)
More Compound Interest (backwards)