Target Mathematics

1.44: Logarithmic equations

4PM1/2/January/2017 — Question 7 · 11 marks

(a) Given that kk is a constant such that
27(x+2)3(3x+5)3x×9(x+2)=k\frac{27^{(x+2)}-3^{(3x+5)}}{3^x\times9^{(x+2)}}=k
find the value of kk. (5)
(b) Find the exact roots of the equation 2log2y+3logy2=72\log_2y+3\log_y2=7. (6)