Determine the value of the unknown in each of the following

Determine the value of the unknown in each of the following equations.

A/ ln(e^7)=t

t=

B/ ln(1/e^k)=5

k=

C/ e^{ln(3x)}=6

x=

D/ ln(e^m)=9

m=

Solution

ln(a^b)=b*ln(a), ln(e)=1 ,e^ln(p)=p

A/ ln(e^7)=t

t=7ln(e)

t=7*1

t=7

B/ ln(1/e^k)=5

ln(e^-k)=5

-k*ln(e)=-5

-k*1=-5

k =5

C/ e^{ln(3x)}=6

3x=6

x=6/3

x=2

D/ ln(e^m)=9

m ln(e)=9

m*1=9

m=9