Ok the first one is: 7^2x+3 = 5^3x-2

I Understand that I can put them in log form, (2x+3)log 7 = (5x-2)log5

but, my teacher mentioned we should use the natural log? So how do I go about doing so?

2. 8^x2 * 4^-3x = 1/2

How I did it:

2^(3x^2) * 2^-6x = 1/2

= 3x^2 * -6x = 1/2

= -18x^3 = 1/2

Some how that doesn't seem right to me.

I thought I could make the bases equal, so I used 2 for both the 8 and the 4. is this correct? does the 1/2 have to have to the same base also?

3. 8-2|6-2x| ≤ -4

-8 -8

= -2|6-2x| ≤ -12

then I divided by 2 on both sides to get |6-2x| ≤ -12

Is that right? should I be dividing by -2 or adding?

4. Last one:

2^x+1 * 8^-x = 4

Same as the first one, I set the bases as 2, So i get

2^x+1 * 2^-3x = 2^2

Should i be doing that for the 4 also? it doesn't seem right again...Thx in advance for the help.