Question

logb a. logc b . loga c = 1​

Answer 1

Required answer:-

Given:-

• $\sf log_{b}(a) \times log_{c}(b) \times log_{a}(c) = 1$

We have to prove this.

Answer:-

Given that,

$\sf log_{b}(a) \times log_{c}(b) \times log_{a}(c) = 1$

❖ Here we have been given to prove this.

Considering LHS,

$\sf log_{b}(a) \times log_{c}(b) \times log_{a}(c)$

As we know that,

$\dag \underline{\boxed{\bf{\blue{log_y(x)=\dfrac{log(x)}{log(y)}}}}}$

$\sf \longrightarrow \dfrac{ log(a) }{ log(b) } \times \dfrac{ log(b) }{ log(c) } \times \dfrac{ log(c) }{ log(a) }$

$\sf \longrightarrow \dfrac{ \blue{ \cancel{log(a)}} }{ \green{\cancel{log(b)}} } \times \dfrac{ \green{ \cancel{log(b)}} }{ \red{ \cancel{log(c)} }} \times \dfrac{ \red{\cancel{log(c)} }}{ \blue{\cancel{log(a)}} }$

$\longrightarrow \sf1$

Considering RHS,

$\sf 1$

As LHS = RHS,

Hence proved!