Target Mathematics

1.46: Logarithmic equations

4PM1/1/June/2017 — Question 7 · 13 marks

(a) Solve log⁡a1024=5\log_a1024=5. (1)
(b) Solve log⁡3(6c+9)=4\log_3(6c+9)=4. (2)
(c) Solve 2(log⁡b25+log⁡b125)=52(\log_b25+\log_b125)=5. (4)
(d) Solve the equations, giving the values of xx and yy to 3 significant figures,
3log⁡2x+4log⁡3y=103\log_2x+4\log_3y=10
log⁡2x−2log⁡3y=1\log_2x-2\log_3y=1
(6)