F.4 Logarithmic Functions

原式 =

(log 36 / log 4) * (log 8^0.5 / log 3) / (log 6 / log 1/9)

=[ log (2^2 * 3^2) / log 2^2) * (0.5 log 2^3 / log 3) / log (2*3) ]* log (3^ -2)

=[ (2log2 + 2log3) / (2 log 2) ] * (1.5 log2 / log 3) / (log 2 + log 3)] * (-2log 3)

= [1 + (log3 / log2)] * 1.5(log2 / log3) / (log2 + log 3) * (-2log3)

= [1.5(log2 / log3) + 1.5] * (-2log 3) / (log2 + log3)

= (- 3 log2 - 3 log3) / (log 2 + log 3)

= - 3(log 2 + log 3) / (log 2 + log 3)

= - 3



2009-12-02 13:59:18 補充：
上面做得較繁

原式 =

(log 36 / log 4) * (log 8^0.5 / log 3) / (log 6 / log 1/9)

=[ log (2^2 * 3^2) / log 2^2) * (0.5 log 2^3 / log 3) / log (2*3) ]* log (3^ -2)

=[ (2log2 + 2log3) / (2 log 2) ] * (1.5 log2 / log 3) / (log 2 + log 3)] * (-2log 3)

= (1 / log 2) * (1.5 log2 / log3) * (-2log 3)

= 1 * 1.5 * (-2)

= - 3

2009-12-02 14:00:18 補充：
原式 =

(log 36 / log 4) * (log 8^0.5 / log 3) / (log 6 / log 1/9)

=[ log (2^2 * 3^2) / log 2^2) * (0.5 log 2^3 / log 3) / log (2*3) ]* log (3^ -2)

=[ (2log2 + 2log3) / (2 log 2) ] * (1.5 log2 / log 3) / (log 2 + log 3)] * (-2log 3)

= (1 / log 2) * (1.5 log2 / log3) * (-2log 3)

= 1 * 1.5 * (-2)

= - 3