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godwin_ibrahim
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Tyro
Asked: 2020-11-11T20:42:11+00:00

What is the value of a if 301_{a}=193_{10} ?

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What is the value of a if 301_{a}=193_{10} ?

number base

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  2. Sengemegz
    Moderator

    Convert base a to base ten
    301_{a}=3\times a^{2}+0\times a^{1}+1\times a^{0}=193_{10}
    \Rightarrow 3a^{2}+1=193
    Subtract 1 from both sides
    \Rightarrow 3a^{2}=193-1
    \Rightarrow 3a^{2}=192
    Divide both sides by 3
    \Rightarrow a^{2}=64
    square root both sides
    \therefore a=8

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