# in logarithms can there be log 4.5 or in any other decimals ?

Please find below the solution to the asked query:

$\mathrm{Yes}.\phantom{\rule{0ex}{0ex}}{\mathrm{log}}_{\mathrm{a}}\left(\mathrm{x}\right)\mathrm{is}\mathrm{defined}\mathrm{when}\mathrm{x}0\mathrm{and}\mathrm{a}0\mathrm{and}\mathrm{a}\ne 1\phantom{\rule{0ex}{0ex}}\mathrm{Hence}\mathrm{log}\left(4.5\right)\mathrm{or}\mathrm{any}\mathrm{log}\left(\mathrm{Positive}\mathrm{Decimal}\right)\mathrm{exists}.$

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