If \(\frac{({a^2b^{-3}c})^{3/4}}{a^{-1}b^4c^5}\) = \(a^p b^q c^r\); what is the value of p+2q?

If 314\(_{10}\) - 256\(_7\) = 340\(_x\), find x.

Evaluate \(log_{\sqrt{2}}4+log_{\frac{1}{2}}16-log_{4}32\)

simplify \(16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\)

If log\(_{x^{1/2}}^{64}\)  = 3, find the value of x