(1)\;log_62+log_6{18}

=log_6{(2×18)}

=log_636

=2

(2)\;log_36-log_3{162}

=log_3{\frac{6}{162}}

=log_3{\frac{1}{27}}

=-3

(3)\;log_6{18}+log_6{200}-2\;log_6{10}

=log_6{18}+log_6{200}-log_6{10^2}

=log_6{(18×200÷100)}

=log_6{36}

=2

(4)\;log_{10}{(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt5})}

=\frac{1}{2}\;log_{10}{(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt5})²}

=\frac{1}{2}\;log_{10}{(3+\sqrt5+2\sqrt{9-5}+3-\sqrt5)}

=\frac{1}{2}\;log_{10}{10}

=\frac{1}{2}

(5)\;2^{2\;log_23}

=2^{log_2{3^2}}

=3^2

=9

(6)\;log_53·log_35

=\frac{log3}{log5}·\frac{log5}{log3}

=1

(7)\;log_2{10}-log_4{25}

=\frac{log10}{log2}-\frac{log25}{log4}

=\frac{log10}{log2}-\frac{2\;log5}{2\;log2}

=\frac{1}{log2}(log10-log5)

=\frac{1}{log2}×log2

=1

(8)\;(log_25)(log_59)(log_9{16})

=\frac{log5}{log2}×\frac{log9}{log5}×\frac{log16}{log9}

=log_2{16}

=4

(9)\;(log_35+log_9{\frac{1}{5}})(log_{25}3+log_5{27})

=log_35×log_{25}3+log_35×log_5{27}\
\;\;\;\;+log_9{\frac{1}{5}}×log_{25}3+log_9{\frac{1}{5}}×log_5{27}

=\frac{log5}{log3}×\frac{log3}{log25}+\frac{log5}{log3}×\frac{log27}{log5}\
\;\;\;\;+\frac{log\frac{1}{5}}{log9}×\frac{log3}{log25}+\frac{log\frac{1}{5}}{log9}×\frac{log27}{log5}

=\frac{log5}{log3}×\frac{log3}{log25}+\frac{log5}{log3}×\frac{log27}{log5}\
\;\;\;\;+\frac{log\frac{1}{5}}{log9}×\frac{log3}{log25}+\frac{log\frac{1}{5}}{log9}×\frac{log27}{log5}\
=\frac{log5}{log3}×\frac{log3}{2\;log5}+\frac{log5}{log3}×\frac{3\;log3}{log5}\
\;\;\;\;+\frac{-log5}{2log3}×\frac{log3}{2log5}+\frac{-log5}{2log3}×\frac{3\;log3}{log5}

=\frac{log5}{log3}×\frac{log3}{2\;log5}+\frac{log5}{log3}×\frac{3\;log3}{log5}\
\;\;\;\;+\frac{-log5}{2log3}×\frac{log3}{2log5}+\frac{-log5}{2log3}×\frac{3\;log3}{log5}\
=\frac{1}{2}+3+\frac{-1}{4}+\frac{-3}{2}

=\frac{7}{4}

Forward

計算或化簡下列各對數值

s = 0 (slider from 0 to 41, step 1)
A = (-0.9356796669820824, 5.577825160434524)