Question

Additional Mathematics

Simplify or express a logarithmic expression in terms of an unknown value.

GIven that lg 2=p , and lg 3 = q , express the following in terms of p and q.

(a) lg 54
(b) lg squareroot 120
(c) lg 3and 3/4

Answer 1

Answer on Question #60016 – Math – Algebra

Question

Simplify or express a logarithmic expression in terms of an unknown value.

Given that $\lg 2 = p$, and $\lg 3 = q$, express the following in terms of $p$ and $q$.

(a) $\lg 54$;

(b) $\lg$ squareroot 120;

(c) $\lg 3$ and $\frac{1}{4}$.

Solution

(a)

$$\lg 54 = \lg 2 \cdot 27 = \lg 2 + \lg 27 = p + \lg 3^3 = p + 3 \lg 3 = p + 3q.$$

(b)

$$\lg \sqrt{120} = \lg 120^{1/2} = \frac{1}{2} \lg (5 \cdot 3 \cdot 8) = \frac{1}{2} (\lg 5 + \lg 3 + \lg 8) = \frac{1}{2} (\lg 5 + q + \lg 2^3) = \frac{1}{2} (\lg 5 + q + 3p).$$

(c)

$$\lg 3\frac{3}{4} = \lg \frac{12 + 3}{4} = \lg \frac{15}{4} = \lg 15 - \lg 4 = \lg (5 \cdot 3) - \lg 2^2 = \lg 5 + \lg 3 - 2 \lg 2 = \lg 5 + q - 2p.$$

Answer: (a) $p + 3q$; (b) $\frac{1}{2} (\lg 5 + q + 3p)$; (c) $\lg 5 + q - 2p$.

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