Question

if 10to to the power x =64 then x =

Answer 1

Answer :


${10}^{x} = 64 \\ \\ = > \: take \: the \: logarithm \: of \: both \: side \\ \\ = > \: log_{10}(10 {}^{x} ) = log_{10}(64) \\ \\ = > \: use \: log_{a}(a {}^{x} ) = x \: and \: simplify \\ \\ = > \: x = log_{10}(64) \\ \\ = > x = log_{10}( {2}^{6} ) \\ \\ = > use \: log_{a}(b {}^{c} ) = c \times log_{a}(b) \: and \: transform \\ \\ = > \: x = 6 log_{10}(2) \\ \\ = > \: x = 1.80618$


HOPE it would help you

Answer 2

$\text{We know that}\\\;\\m^x=n\implies x=\log_mn\\\;\\Similarly,\\\;\\10^x=64\implies x=\log_{10}64\\\;\\x=\log_{10}2^6\\\;\\x=6\log_{10}2\\\;\\x=6\times0.3010\\\;\\x=1.806\\\;\\\textbf{x = 1.806}\\\;\\Note:-\\\;\\1.\;\;\log m^n=n\log m\\\;\\2.\;\;\log_{10}2=0.3010$