1. Find the value of x in the following problem. 8^3x-1=64

To solve the equation $8^{3x-1}=64$, we can rewrite both sides of the equation with the same base.<br /><br />$8^{3x-1}=64$<br /><br />Since $8=2^3$ and $64=2^6$, we can rewrite the equation as:<br /><br />$(2^3)^{3x-1}=2^6$<br /><br />Simplifying the left side, we get:<br /><br />$2^{9x-3}=2^6$<br /><br />Since the bases are the same, we can set the exponents equal to each other:<br /><br />$9x-3=6$<br /><br />Solving for x, we get:<br /><br />$9x=9$<br /><br />$x=1$<br /><br />Therefore, the value of x in the equation $8^{3x-1}=64$ is 1.