Question

Simplify log3(2)*log4(3)*log5(4)*log6(5)......*log20(19)

Answer 1

Please see the attachment

Answer 2

The value of given expression is $\log_{20}2$.

Step-by-step explanation:

The given expression is

$\log_3(2)\cdot \log_4(3)\cdot \log_5(4)\cdot \log_6(5)\cdot ...\cdot \log_{20}(19)$

We need to find the value of given expression.

According to the property of log.

$\log_xy=\dfrac{\log_ ay}{\log_a x}$

Using the above property of log the given expression can be rewritten as

$\dfrac{\log 2}{\log 3}\cdot\dfrac{\log 3}{\log 4}\cdot\dfrac{\log 4}{\log 5}\cdot\dfrac{\log 5}{\log 6}\cdot....\cdot \dfrac{\log 19}{\log 20}$

Cancel out the common factors.

$\dfrac{\log 2}{\log 20}$

$\log_{20}2$

Therefore, the value of given expression is $\log_{20}2$.

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