Its About Logarithm!

Algebra Level 2

If log ⁡ 10 x 324 = 4 \log_{10} x^{324} = 4 , what is x x ?


The answer is 1.0288.

Maruf Ahmed by Maruf Ahmed , 17, Bangladesh

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1 solution

log ⁡ 10 x 324 = 4 324 log ⁡ 10 x = 4 log ⁡ 10 x = 1 81 ⟹ x = 1 0 1 81 ≈ 1.0288 \begin{aligned} \log_{10} x^{324} & = 4 \\ 324 \log_{10} x & = 4 \\ \log_{10} x & = \frac 1{81} \\ \implies x & = 10^{\frac 1{81}} \approx \boxed{1.0288} \end{aligned}

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