What is the limit as x approaches 2 of log_{10x}(x) ?

The limit as x approaches 2 of log_{10x}(x) is log_{20}(2)

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limit as x approaches 2 of log_{10x}(x)

x \to 2 lim (lo g_{10 x} (x))

lo g_{20} (2)

Decimal

0.23137 \dots

Solution steps

x \to 2 lim (lo g_{10 x} (x))

Plug in the value

x = 2

= lo g_{10 \cdot 2} (2)

Simplify

= lo g_{20} (2)

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What is the limit as x approaches 2 of log_{10x}(x) ?
The limit as x approaches 2 of log_{10x}(x) is log_{20}(2)