How do you calculate ${log}_{2} 56 - {log}_{4} 49$ $Log_2 56 - log_4 49$ ?

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Answer 1 · 2016-08-09T05:20:53

${log}_{2} 56 - {log}_{4} 49 = 3$ $log_2 56-log_4 49 = 3$

Expression $= {log}_{2} 56 - {log}_{4} 49$ $=log_2 56-log_4 49$

First put the each term on the same base. I will choose ${log}_{2}$ $log_2$

We know that: ${log}_{b} x = \frac{{log}_{a} x}{{log}_{a} b}$ $log_b x = (log_a x)/(log_a b)$

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

Hence: ${log}_{4} 49 = \frac{{log}_{2} 49}{{log}_{2} 4}$ $log_4 49 = (log_2 49)/(log_2 4)$

$= \frac{{log}_{2} 49}{2} = {log}_{2} 49^{\frac{1}{2}}$ $= (log_2 49)/2 = log_2 49^(1/2)$

$= {log}_{2} \sqrt{49} = {log}_{2} 7$ $= log_2 sqrt(49) = log_2 7$

Therefore, Expression $= {log}_{2} 56 - {log}_{2} 7 = {log}_{2} (\frac{56}{7})$ $= log_2 56 - log_2 7 = log_2 (56/7)$
$= {log}_{2} 8$ $=log_2 8$

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

How do you calculate log256−log449Log_2 56 - log_4 49?