The product of all the solution satisfying the equation $x^{{log}_{10} x} = \frac{10000}{x^{3}}$ , is -

\frac{1}{10}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{100}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{1000}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{10000}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{1}{10000}$
$x^{l o g_{10} x} = \frac{10^{4}}{x^{3}}$

$l o g_{10} x^{l o g_{10} x} = l o g_{10} \frac{10^{4}}{x^{3}}$

$l o g_{10} x . l o g_{10} x = l o g_{10} 10^{4} - l o g_{10} x^{3}$

$(l o g_{10} x)^{2} = 4 l o g_{10} 10 - 3 l o g_{10} x$

Let $l o g_{10} x = t$

$t^{2} + 3 t - 4 = 0$

$(t - 1) (t + 4) = 0$

$t = 1; t = - 4$

$l o g_{10} x = 1$ or $l o g_{10} x = - 4$

$x = 10^{1} = 10$ or $x = 10^{- 4}$

$x = 10$ or $x = \frac{1}{10000}$

Suggest Corrections

Similar questions

Write the corresponding numeral for each of the following:

(i) $6 \times 10000 + 2 \times 1000 + 5 \times 100 + 8 \times 10 + 4 \times 1$

(ii) $5 \times 100000 + 8 \times 10000 + 1 \times 1000 + 6 \times 100 + 2 \times 10 + 3 \times 1$

1, \frac{1}{10}, \frac{1}{100}, \frac{1}{1000}, \frac{1}{10000}, . .

100 \times 8 + 10 \times 5 + 9

10000 \times 1 + 100 \times 5 + 10 \times 2

1000 \times 5 + 10 \times 1 + 3

100000 \times 3 + 1000 \times 1 + 10 \times 3

p H = 7.4

p K_{a}

A^{-}

H A

1 L = ____ mL

Join BYJU'S Learning Program