Question

log↓10 100=x please explain​

Answer 1

Answer:

$log_{10}(100 ) \\ = > log_{10}(10 \times 10 ) \\ = > log_{10}( {10}^{2} ) \\ we \: know \: that \: \\ \: log_{x}( {a}^{m} ) = m \: log_{x}(a) \\ so \: we \: have \: \\ 2 log_{10}(10) \\ = > 2 \times 1 \\ since \: log_{a}(a) = 1 \\ \: = > 2 \\ \: therefore \: log_{10}(100 ) = 2$

Alternative Method:-

$given \: that \: \: \\ log_{10}(100 ) \: \\ let \: log_{10}(100 ) = x \\ = > {10}^{x } = 100 \\ since \: log_{a}(n) = x = > {a}^{x} = n \\ = > {10}^{x} = \: {10}^{2} \\ = > x = 2 \\ \: since \: the \: bases \: are \: equal \: then \: exponents \: must \: be \: equal$

Answer 2

Refer the given attachment