Questions about exponents and absolute values
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
= -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.