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Algebra Level 1

If log x ( 1 0 6 ) = 6 \large \log_ x(10^6) =6 , find the value of x x .

10 6 90 9 100

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2 solutions

Pranshu Gaba
Apr 20, 2016

Relevant wiki: Properties of Logarithms - Basic

We can rewrite the left hand side as

log ( 1 0 6 ) log x = 6 \frac{\log (10^6)}{\log x} = 6

We can rearrange the terms to make log x \log x the subject of the formula.

log x = 1 6 × log ( 1 0 6 ) \log x = \frac{1}{6} \times \log (10^6)

Using properties of logarithms , we get log x = log 10 \log x = \log 10 , therefore x = 10 x = 10 . _\square

log x ( 1 0 6 ) = 6 \log_x (10^{6}) = 6

x 6 = 1 0 6 \implies x^{6} = 10^{6}

x = 10 x = 10

Therefore, x x equals 10. \boxed {10.}

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