Needing some help with Logarithms and Natural Base e problem

[Simple Beauty]

I somewhat get the work for the most part but there were some certain problems that have given me some problems that hopefully one of you can help me with. I would greatly appreciate it.


4^(3x-2)=1/8 <---I know 'x' equals to 1/6, a friend of mine inputted the problem into his math program and that's the answer that came up, but I have absolutely no idea how it came to that answer or even where to begin really with this one.

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(600)/(1+e^-x)=525 <----I attempted this one and I thought I could do it but when I came to an answer, it didn't match with and of the multiple choice answers, so I don't know where I went wrong

600 - 1 + e^-x=525
600 + e^-x=526
e^-x = -74
ln e^-x = ln -74
-x = ln 74
x = ln 74
x = 4.304

The multiple choices answers that were given were:

A) -0.762
B) 1.946
C) 1.882
D) -0.629

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Log-base-2 x +log-base-2 (x - 15) = 4 <--- This one I started on but I got stuck, I didn't know where to take it

Log-base-2 x +log-base-2 (x - 15) = 4
Log-base-2 (x)(x-15) = 4
Log-base-2 (x^2) - 15x = 4
Log-base-2 (x^2) - 15x + 4 = 0

I didn't quite know where to take it after that or if I was even doing it correctly.

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I would greatly appreciate it if anyone could help me on these. I really want to learn how to do them and correct my mistakes so i'll know for my test coming up on it.

 

[pka]

For your #1:
\(\displaystyle \L
\left. \begin{array}{l}
4^{3x - 2} = \left( {2^2 } \right)^{3x - 2} = 2^{6x - 4} \\
\frac{1}{8} = 2^{ - 3} \\
\end{array} \right\} \Rightarrow \quad 2^{6x - 4} = 2^{ - 3} \Rightarrow \quad 6x - 4 = - 3\)

 

[Simple Beauty]

For your #1:
\(\displaystyle \L
\left. \begin{array}{l}
4^{3x - 2} = \left( {2^2 } \right)^{3x - 2} = 2^{6x - 4} \\
\frac{1}{8} = 2^{ - 3} \\
\end{array} \right\} \Rightarrow \quad 2^{6x - 4} = 2^{ - 3} \Rightarrow \quad 6x - 4 = - 3\)

Thank you so much for your help! I greatly appreciate it <3