Discussion

Question:

If $\log_{10}$ x - $\log_{10}$ $\sqrt[3]{x}$ = 6 $\log_{x}$ 10 then the value of x is

Explanation:

$\log_{10}$ x - $\log_{10}$ $\sqrt[3]{x}$ = $\frac{6}{\log_{10} x}$

∴ $\log_{10}$ x - $\frac{1}{3}$ $\log_{10}$ x = $\frac{6}{\log_{10} x}$

$\log_{10}$ x = a

∴ a² - $\frac{1}{3}$ a² = 6

∴ a² = 9

∴ a = ±3

As log cannot be negative a = 3

∴ $\log_{10}$ x = 3

∴ x = 1000

Hence, option (d).

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