If log 3 = 0.477 and (1000)^{x} = 3,then x eq | vedclass

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(C) Given $\log 3 = 0.477$ and $(1000)^{x} = 3$.Taking $\log_{10}$ on both sides:$\log_{10}(1000)^{x} = \log_{10} 3$Using the property $\log(a^b) = b

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$0.159$

Vedclass · Answer

(C) Given $\log 3 = 0.477$ and $(1000)^{x} = 3$.Taking $\log_{10}$ on both sides:$\log_{10}(1000)^{x} = \log_{10} 3$Using the property $\log(a^b) = b \log a$:$x \log_{10}(10^3) = \log_{10} 3$Since $\log_{10}(10^3) = 3$:$3x = \log_{10} 3$$x = \frac{1}{3} \log_{10} 3$Substituting the given value $\log 3 = 0.477$:$x = \frac{0.477}{3} = 0.159$

If $\log 3 = 0.477$ and $(1000)^{x} = 3$,then $x$ equals

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