已知:log以18为底5的对数=a,18的b次方=2,求log以45为底36的对数的值用a和b的式子来表示

log以18为底5的对数=a,记为 log(18)(5)=a
18^b=2 两边取以18为底的对数,得 log(18)(2)=b
log(45)(36)
=log(18)(36)/log(18)(45) {换底公式}
=log(18)(18*2) / log(18)(5* 9)
=(log(18)(18)+log(18)(2)) / (log(18)(5) + log(18)(9)) {利用log()(A*B)=log()(A)+log()(B)}
=(1+b) / (a + log(18)(18/2)) {有已知条件代换,并利用底的对数是1的性质}
=(1+b) / (a + log(18)(18)-log(18)(2)) {利用log()(A/B)=log()(A)-log()(B)}
=(1+b) / (a +1-b)