(ln5.9546)/(ln1.1012)

ln is the natural logarithm

In fact, it is log(1.1012, 5.9546). The definition is to find this n, and then use the base-changing formula

Remember some formulas and you will know what is going on

When a^n=b, then n=log(a, b) (a is a subscript, agt; 0, bgt; 0, a!=1)

ln(b)=log(e, b) (e is a natural constant)

lg(b)=log(10,b)

log(a,b)=log(c,b)/log(c,a)

log(a,b ^n)=n*log(a,b)

log(a,b*c)=log(a,b) log(a,c)

log(a , b/c)=log(a,b)-log(a,c)

The formula changes to

n

=log( 1.175/1.067, 51900/8176)

=lg(51900/8176)/(lg(1.175/1.067))

=lg(51900/8176)/(lg(1.175 )-lg(1.067))

In fact, it can also be written as ln. According to the base changing formula, any base can be used, but ln and lg are commonly used