how do you graph and solve logarithmic and exponential equations

Question

Solving

 

3e^(-2x)=12

 

2^(x+1)+3=9

 

2+ln(x+3)=13

 

Graphing

 

2+log₂(x+1)

 

-log_1/2x

 

-2+ln (x-3)

 

2^(x+1)-3

 

log₂(x+2)+4

 

Answer 1

3e^(-2x)=12

e^(-2x)=4

ln[e^(-2x)]=ln(4)

-2x=1.38629436112

x=-0.69314718056

 

2^(x+1)+3=9

2^(x+1)=6

(2^x)(2^1)=6

(2^x)=3

log(2^x)=log(3)

xlog(2)=log(3)

(x)(0.30102999566)=0.47712125472

x=(0.47712125472)/(0.30102999566)

x=1.584962502

 

2+ln(x+3)=13

ln(x+3)=11

ln(x)=loge(x)=y implies e^y=x

e^11=x+3

59,874.1417152=x+3

x=59,871.1417152