Use logarithms only to evaluate, correct to 4 decimal places:

Using logarithm tables:

• $\log(12.78) = 1.1065$
• $\sin 33.45^\circ = 0.5512$ $\log(\sin 33.45^\circ) = \log(0.5512) = \bar{1}.7413$
• $\log(9.063) = 0.9572$

$$\log X = \frac{1}{3} (1.1065 + \bar{1}.7413 - 2 \times 0.9572)$$ $$\log X = \frac{1}{3} (1.1065 + (-1 + 0.7413) - 1.9144)$$ $$\log X = \frac{1}{3} (1.1065 - 0.2587 - 1.9144)$$ $$\log X = \frac{1}{3} (0.8478 - 1.9144)$$ $$\log X = \frac{1}{3} (-1.0666)$$

$$-0.3555 = -1 + 0.6445$$

So, $\log X = \bar{1}.6