Exponential Equations Solve a 5 ln x 10 b ln 4x 15 c log 2

Exponential Equations

Solve:

a) 5 ln x = 10

b) ln (4x) = 1.5

c) log (2-x) = 0.5

a) 5 ln x=10

lnx=2

convertint it in exponential form

x=e^2

b) ln 4x=1.5

writing it in exponential form

4x=e^1.5

x=(e^1.5)/4

c) log(2-x)=0.5

writing it in exponential form

2-x=10^0.5

x=2-10^0.5

d) log₆(2x+4)=2

converting it in exponential form

2x+4=6^2

2x+4=36

2x=32

x=16

e) log₄(x^3 + 37)=3

converting it in exponetial form

x^3 + 37=4^3

x^3=64-37=27

x=3

f) log₃(x+5)(x-3)=2

converting it in exponential form we get

(x+5)(x-3)=3^2=9

x^2 +2x-15-9=0

x^2+2x-24=0

(x+6)(x-4)=0

x=-6,4