# Two BB Math Questions

<p>Page 397 Question #9:</p>

<p>If 2 ^ (2x) = 8 ^ (x-1), what is the value of x?</p>

<p>Page 400 Question #18:</p>

<p>For the answer, how do you know that III is true?</p>

<p>Thank yoo.</p>

<p>I forget how to do the first one, but keep in mind that with a TI-89 you can just plug it in and use the solver (if you're using one).</p>

<p>For the first one:
8^(x-1) = 2^(3x-3)
Exponents equal each other, so 2x=3x-3, so x=3.</p>

<p>Second one:
If b is the y value for a and lies in the shaded region, it must be lower than f(a) graphed. Sorry if that's a poor explanation...</p>

<p>sylvie is wrong in the example it's 2^(3x-3) = 2x</p>

<p>8 is 2^3
so 3 times (x-1) and then its
2x=3x-3
you push them around until you get x by itself on one side
so it would be
x=3</p>

<p>people clearly got this right, but i'm not sure i could have learned how to do it from their explanations if i hadn't done it myself. </p>

<p>given: 2^(2x) = 8^(x-1)
8 = 2^3, as you know
so replacing the 8 with this in the original equation
2^(2x) = (2^3)^(x-1)</p>

<p>recall (x^y)^z = x^(yz), so using that on the right-hand side of the above equation
2^(2x) = 2^(3x-3)</p>

<p>if a^x = a^y, then x=y because it has to for a^x to equal a^y as long as a≠1 (and a=2, so it works). set 2x=3x-3 and solve.</p>