Answer:
Prove that
[tex]log_{a}(b) \times log_{b} (c)=log_{a} (c)[/tex]
To demonstarte this, we need to use the following property
[tex]log_{b}(x)=\frac{log_{d}(x) }{log_{d}(b) }[/tex]
So, in this case,
[tex]log_{b}(c)=\frac{log_{a}(c) }{log_{a}(b) }[/tex]
Repling this in the first expression, we have
[tex]log_{a}(b) \times\frac{log_{a}(c) }{log_{a}(b) }=log_{a} (c)[/tex]
Multiplying and dividing, we have
[tex]\frac{log_{a}(b) \times log_{a}(c) }{log_{a}(b) }=log_{a}(c)[/tex]
[tex]\therefore log_{a}(c)= log_{a}(c)[/tex]
So, by using one property, we can demostrate the given expression.
