WAEC 2016 · Paper 2 · Q1

Indices, logarithms & surds

(a)
If $8^m + 2^{3m} = \frac14$ , find the value of $m$ .
(b)
Given that $\log_4 15 = x$ , find, correct to three decimal places, the value of $x$ .

Worked solution (try it first)

(a)

Write $8$ as a power of 2: $8^m = (2^3)^m = 2^{3m}$ .
So the left side is $2^{3m} + 2^{3m} = 2 \times 2^{3m}$
$= 2^{3m + 1}$ .
Write the right side as a power of 2: $\frac14 = 2^{-2}$ .
Compare the indices: $3m + 1 = -2$ , so $3m = -3$ and $m = -1$ .

(b)

Change the base to 10: $x = \log_4 15 = \dfrac{\log 15}{\log 4}$ .
$x = \dfrac{1.1761}{0.6021} = 1.953$ to three decimal places.

Report a problem with this question