Use natural logarithms to solve the equation. Round to the nearest thousand. 3e^4x-12=29. HAve no idea how to solve this, help?

Question

campbell_st · Answer

is the equation.

1. $$3e^{4x -12} = 29$$

or 

2. 

$$3e^{4x} - 12 = 29$$

anonymous · Answer

@campbell_st number 2 :)

campbell_st · Answer

ok... start by adding 12 to both sides of the equation 

$$3e^{4x} = 41$$

next divide by 3

$$e^{4x} = \frac{41}{3}$$

now take the ln of both sides

$$4x = \ln(\frac{41}{3})$$

now solve for x

anonymous · Answer

@campbell_st so you divide both numbers by 4 and they come out as a decimal correct?

campbell_st · Answer

thats correct

anonymous · Answer

@campbell_st idk if i divided it correctly but would it be 3.4166?

campbell_st · Answer

well you seem to have an error... 

what is 

ln(41/3) = 

then divide that answer by 4

anonymous · Answer

@campbell_st so ln(43/3) is 2.61495? so then it would equal 0.6537?

campbell_st · Answer

yep... thats what I calculated x to be... you can check it by substitution 

$$3e^{4 \times 0.6537} - 12 = 29$$

anonymous · Answer

@campbell_st  thanks so much you helped me out a lot!

campbell_st · Answer

no problem... just make sure you don't use logs to early in this type of question... 

good luck