1. ## log questions

I have a few more log questions that I am stuck on. Any help is appreciated. Thanks

1. Solve the the unknown value: log(ln(x))=0

2. If g(x)=ln(x), find g(e^6.45)

3. solve: 4^x+2=8
(it is 4 to the x+2 power)

thanks again

2. Originally Posted by mamajen

3. solve: 4^x+2=8
(it is 4 to the x+2 power)
$4^{x+2}=8$

$(2^2)^{x+2}=2^3$

$2^{2(x+2)}=2^3$

$2(x+2)=3$

Can you finish it?

3. the question is in exponential form and needs to be solved for log form. I can solve for x but that doesn't give me the log form that it is wanting. here is how far i have gotten.....
log base 4 (8) = x+2
I am lost after that.
I am not sure if that is how I need to solve it either.
I have written in my notes that if it is in exponential form that you need to take the log base 10 of both sides. So I am not sure if I should solve it the way I have above or if I should go this way....
log4x+2=log8

4. Consider $a^b = c \implies b= \log_ac$

Therefore

$4^{x+2}=8$

$x+2=\log_48$

$x=\log_4(8) -2$

How is this?

5. ok after much thinking i figured this out.
you take the ln of both sides which will give you......
(x+2) * ln(4)=ln(8) which then turns into.....

x+2= ln8/ln4 then subtract the 2 on both sides gives you

x= ln8/ln4 - 2

x= -.5