Question

If $7^x=1000$ then, x=_____.

• A. $\frac{3}{log7}$
• B. $\frac{9}{3log7}$
• C. $\frac{7}{log3}$
• D. $\frac{3}{7}$

Answer 1

The correct option is A $\frac{3}{log7}$

$7^x=1000$
$7^x={10}^3$
Take the common logarithm of both sides, and take advantage of the property of the logarithm of a power
$log{7}^x=log{10}^3$
$xlog7=3log10$
$xlog7=3\times 1$
As, $lo{g}_{10}10=1$
So,
$xlog7=3$
$x=\frac{3}{log7}$