<p>The real value of <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> such that <img alt="$64^{x-1}$" height="15" src="https://latex.artofproblemsolving.com/6/9/6/696167aeaffaf683c282049d633360ae4b9b27eb.png" width="41" /> divided by <img alt="$4^{x-1}$" height="15" src="https://latex.artofproblemsolving.com/c/a/5/ca591548448b794ea79a3054c89207caa93e0a54.png" width="32" /> equals <img alt="$256^{2x}$" height="15" src="https://latex.artofproblemsolving.com/3/f/7/3f76a18b37f9747bf9484d388359f961c37e9076.png" width="40" /> is:</p> <p><img alt="$\text{(A) } -\frac{2}{3}\quad\text{(B) } -\frac{1}{3}\quad\text{(C) } 0\quad\text{(D) } \frac{1}{4}\quad\text{(E) } \frac{3}{8}$" height="38" src="https://latex.artofproblemsolving.com/3/d/e/3de675cfeed51cddcb226fcfc092ef3c8b237620.png" width="323" /></p>

Question No: 456

The real value of $x$ such that $64^{x-1}$ divided by $4^{x-1}$ equals $256^{2x}$ is:

$\text{(A) } -\frac{2}{3}\quad\text{(B) } -\frac{1}{3}\quad\text{(C) } 0\quad\text{(D) } \frac{1}{4}\quad\text{(E) } \frac{3}{8}$

Editorial

Tags: Algebra

Question Details