Solve the following equations log3x 6 log3x 3 6ex 12 Wri

Solve the following equations: log_3(x - 6) + log_3(x) = 3. 6e^x = 12. (Write the answer in terms of logarithms, or round it to the nearest hundred.)

Solution

log₃(x-6)+log₃(x)=3

log₃(x(x-6))=3

x(x-6)=3³=27

x²-6x-27=0

(x-9)(x+3)=0

x=9,-3

log cant take negative values

Therefore correct answer is x=9

b. 6e^x=12

e^x=2

Taking ln ln both sides

x=ln 2

x=0.69