Question

If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512

Answer 1

3.875 is the answer 
log512÷log5 
log2^{9} ÷㏒(10÷2)
9㏒2÷ ㏒10 - ㏒2
9 * 0.3010 / 1 - 0.3010 (rules of logarithms log 10 = 1)
2.709 ÷ 0.699
shift the decimal places 
2709/699
3.876 

Answer 2

The value is $\log_5 512=3.8755$

Step-by-step explanation:

Given : If $\log 2 = 0.3010$ and $\log 3 = 0.4771$

To find : The value of $\log_5 512$ ?

Solution :

Expression $\log_5 512$

Apply logarithmic property, $\log_b a=\frac{\log a}{\log b}$

$\log_5 512=\frac{\log 512}{\log 5}$

$\log_5 512=\frac{\log 2^9}{\log (\frac{10}{2})}$

Apply logarithmic property, $\log a^x=x\log a$ and $\log (\frac{a}{b})=\log a-\log b$

$\log_5 512=\frac{9\log 2}{\log 10-\log 2}$

Substitute the value,

$\log_5 512=\frac{9(0.3010)}{1-0.301}$

$\log_5 512=\frac{2.709}{0.699}$

$\log_5 512=3.8755$

Therefore, the value is $\log_5 512=3.8755$

#Learn more

If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

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