如果log以3为底[log以4为底（log以5为底的a次方）]等于log以4为底[log以3为底（log以5为底的b次方）]等于0,则b 分之a的值为?

题目

如果log以3为底[log以4为底（log以5为底的a次方）]等于log以4为底[log以3为底（log以5为底的b次方）]等于0,则b 分之a的值为?

答案

log_3[log_4(log_5(a))] = 0 (1)
log_4[log_3(log_5(b))] = 0 (2)
(1) => log_4(log_5(a)) = 1
=> log_5(a) = 4
=> a = 5^4
(2) => log_3(log_5(b)) = 1
=> log_5(b) = 3
=> b = 5^3
所以,a/b = 5
式中,log_5(a)表示以5为底的对数,5^3表示5 的三次方