Question

Applying the concepts. Need help finding the value.

Answer 1

we can use formula

$log_ab=\frac{ln(b)}{ln(a)}$

$log_23*log_34*log_45*log_56*log_6 7 *log_7 8=\frac{ln(3)}{ln(2)}*\frac{ln(4)}{ln(3)}*\frac{ln(5)}{ln(4)}*\frac{ln(6)}{ln(5)}*\frac{ln(7)}{ln(6)}*\frac{ln(8)}{ln(7)}$

now, we can cancel terms

and then we can simplify it

$log_23*log_34*log_45*log_56*log_6 7 *log_7 8=\frac{ln(8)}{ln(2)}$

$log_23*log_34*log_45*log_56*log_6 7 *log_7 8=\frac{ln(2^3)}{ln(2)}$

$log_23*log_34*log_45*log_56*log_6 7 *log_7 8=\frac{3ln(2)}{ln(2)}$

now, we can simplify it

and we get

$log_23*log_34*log_45*log_56*log_6 7 *log_7 8=3$...........Answer