How do you calculate $Log_2 56 - log_4 49$ ?

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Answer 1 · 2016-08-09T05:20:53

$log_2 56-log_4 49 = 3$

Expression $=log_2 56-log_4 49$

First put the each term on the same base. I will choose $log_2$

We know that: $log_b x = (log_a x)/(log_a b)$

To change the base of $log_4 49$ to $log_2$
We have $a=2, b=4 and x =49$

Hence: $log_4 49 = (log_2 49)/(log_2 4)$

$= (log_2 49)/2 = log_2 49^(1/2)$

$= log_2 sqrt(49) = log_2 7$

Therefore, Expression $= log_2 56 - log_2 7 = log_2 (56/7)$
$=log_2 8$

$= 3$ (Since $8=2^3$ )

How do you calculate Log_2 56 - log_4 49Log_2 56 - log_4 49?