Lesson Summary (February 27, 2013)

Worksheet A02d
6) log₅(log₃x)=log₁₀₀100
log₅(log₃x)=1
log₃x=5¹
x=3⁵
  =243

7) log₅x=a            log√5y=b
express xy² as a power of 5
x=5ª                      y=√5ᵇ
                               =5^b/2

xy²=5ª x 5^2b/2
     =5^a+2b/2
     =5^a+b

*Don't cancel your answer even if it seems wrong (sometimes it might be correct) only cancel after realising the mistake and redoing.

Worksheet A02e
9) 6ⁿ + 6^n+1 + 6^+2
= 6ⁿ+6ⁿ6+6ⁿ6²
= 6ⁿ(1+6+36)
= 6ⁿ(43)
∴divisible by 43 for all natural values of n.

11) log₅(5-4x) = log√5(2-x)
                        = log₅(2-x)/log₅5^1/2
                        = log₅(2-x)/(1/2)
                        = log₅(2-x)²

5-4x = (2-x)²
        = 4 - 4x + x²
x²=1
x=±1

* Sorry for the late post