2x=10{2}^{x}=10
1
Use Definition of Common Logarithm: ba=x{b}^{a}=x if and only if logb(x)=alog_b(x)=a.
x=log⁡210x=\log_{2}{10}

2
Use Change of Base Rule: log⁡bx=log⁡axlog⁡ab\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}.
x=log⁡10log⁡2x=\frac{\log{10}}{\log{2}}

3
Use Rule of Ten: log⁡10=1\log{10}=1.
x=1log⁡2x=\frac{1}{\log{2}}

Done

Decimal Form: 3.321928

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