Given $2 l o g_{10} x + 1 = l o g_{10} 250$ , find :

(i) $x$

(ii) $l o g_{10} 2 x$

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Solution

2log x + log 10 = log 250
1-
log x² + log 10 = log 250
log (10x²) = log 250
10x² = 250
x² = 250/10
x² = 25
x = $\sqrt{25}$
x = 5

2-
(ii) $l o g_{10} 2 x$
$l o g_{10} 2 \times 5$ = $l o g_{10} 10$ = 1

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