1.7: Common logarithms; hence solve for a

0606/12/M/J/18 — Question 9 · 9 marks · Log laws, Change of base, Equations

(a)(i)
Solve lg⁡x=3\lg x = 3.
[1]
(a)(ii)
Write lg⁡a−2lg⁡b+3\lg a - 2\lg b + 3 as a single logarithm.
[3]
(b)(i)
Solve x−5+6x=0x - 5 + \dfrac{6}{x} = 0.
[2]
(b)(ii)
Hence, showing all your working, find the values of aa such that log⁡4a−5+6log⁡a4=0\log_{4} a - 5 + 6\log_{a} 4 = 0.
[3]