If $x = l o g 0.6; y = l o g 1.25$ and $z = l o g 3 - 2 l o g 2$ , find the values of :

(i) $x + y - z$

(ii) $5^{x + y - z}$

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Solution

$x = l o g 0.6, y = l o g 1.25, z = l o g 3 - 2 l o g 2$

$z = l o g 3 - 2 l o g 2$
$z = l o g 3 - l o g 2^{2}$
= $l o g \frac{3}{4}$
= $l o g 0.75$

(i) $x + y - z = l o g 0.6 + l o g 1.25 + l o g 0.75$ $\frac{0.6 \times 1.25}{0.75}$
$x + y - z = l o g$ $\frac{0.6 \times 1.25}{0.75}$
$x + y - z = l o g 1$
$x + y - z = 0$

(ii) $5^{x + y - z}$ = $5^{0}$ = 1

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