Question

Simplify without use of Log tables 8log2- 2log4/log2

Answer 1

8log2-2log4/log2

log2^8-log4^2/log2

log256-log16/log2

log(25/16)/log2

50/16

Answer 2

Answer:

$\frac{8\log 2-2\log 4}{\log 2}=4$

Step-by-step explanation:

Given : Expression $\frac{8\log 2-2\log 4}{\log 2}$

To find : Simplify the expression without using log tables ?

Solution :

Expression $\frac{8\log 2-2\log 4}{\log 2}$

Applying logarithmic identity, $a\log b=\log b^a$

$=\frac{\log 2^8-\log 4^2}{\log 2}$

$=\frac{\log 256-\log 16}{\log 2}$

Applying logarithmic identity, $\log a-\log b=\log (\frac{a}{b})$

$=\frac{\log (\frac{256}{16})}{\log 2}$

$=\frac{\log (16)}{\log 2}$

Applying logarithmic identity, $\frac{\log_x a}{\log_x b}=\log_b a$

$=\log_2 (16)$

$=\log_2 (2)^4$

Applying logarithmic identity, $\log_a (a)^x=x$

$=4$

Therefore, $\frac{8\log 2-2\log 4}{\log 2}=4$