WAEC 2012 · Paper 2 · Q1

(a)
Without using tables or calculators, simplify $\dfrac{\log7\sqrt7 - \log5\sqrt5}{\log1.4}$ .

Worked solution (try it first)

Write the surds as powers: $7\sqrt7 = 7^1 \times 7^{\frac12}$
$= 7^{\frac32}$ and $5\sqrt5 = 5^{\frac32}$ .
Bring the powers down in front: the top is $\frac32\log 7 - \frac32\log 5 = \frac32(\log 7 - \log 5)$ .
Write the bottom the same way: $1.4 = \frac75$ , so $\log 1.4 = \log 7 - \log 5$ .
The bracket $(\log 7 - \log 5)$ cancels, so the value is $\dfrac32$ .