(1)\;log\frac{5}{9}-log\frac{3}{7}+log\frac{27}{35}

=log\left(  \frac{5}{9}÷\frac{3}{7}×\frac{27}{35} \right) 

=log\left( \frac{5}{9}×\frac{3}{7}×\frac{27}{35}  \right) 

=log1

=0

(2)\;\frac{1}{3}log_2\frac{27}{8}-log_224+3log_2\sqrt[3]{2}

=log_2\left(  \frac{27}{8} \right) ^\frac{1}{3}-log_224+log_2(\sqrt[3]{2})³

=log_2\frac{3}{2}-log_224+log_22

=log_2\left(\frac{3}{2}÷24×2   \right) 

=log_2\frac{1}{8}=-3

(3)\;(log_23+log_49)(log_34+log_92)

=\left( \frac{log3}{log2}+\frac{log9}{log4}  \right) \left(\frac{log4}{log3}+\frac{log2}{log9}   \right) 

=\left( \frac{log3}{log2}+\frac{2log3}{2log2}  \right) \left(\frac{2log2}{log3}+\frac{log2}{2log3}   \right) 

=\left( 2·\frac{log3}{log2}  \right) \left( \frac{5}{2} ·\frac{log2}{log3} \right) 

=5

(4)\;(log_23+log_89)(log_38+log_92)

=log_23\;log_38+log_89\;log_38+log_23\;log_92+log_89\;log_92

=log_28+log_89\;log_9{64}+log_49\;log_92+log_82

=3+log_8{64}+log_42+\frac{1}{3}

=\frac{10}{3}+2+\frac{1}{2}

=\frac{35}{6}

Forward

對數的計算

s = 0 (slider from 0 to 21, step 1)
A = (-0.35785687600116395, 4.984397497857789)