Alg9.4.4

Rule of change of base,if a and b not equal to 1 and m is a positive real number, then $\log_a(m)=\log_b(m)\cdot\log_a(b)\,$

Let

$log_a(m)=x, \log_b(m)=y,\log_a(b)=z\,$

$m=a^x,m=b^y,b=a^z\,$

Hence from the above

$a^x=m=b^y=(a^z)^{y}=a^{yz}\,$

From the above,

$x=yz\,$

Substituting the values of x,y,z

$\log_a(m)=\log_b(m)\cdot\log_a(b)\,$