2.9: Logs from a power relation; two index equations

0606/22/M/J/17 — Question 7 · 7 marks · Log laws, Indices, Equations

(a) Given that a7=ba^{7} = b, where aa and bb are positive constants, find:
(a)(i)
log⁡ab\log_{a} b
[1]
(a)(ii)
log⁡ba\log_{b} a
[1]
(b)
Solve the equation log⁡81y=−14\log_{81} y = -\dfrac{1}{4}.
[2]
(c)
Solve the equation 32x2−14x2=16\dfrac{32^{x^{2} - 1}}{4^{x^{2}}} = 16.
[3]