Question

If log2=0.3010 log3=0.4771 and log7=0.8451 find the value of log 105

Answer 1

Answer:

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Answer 2

The value is $\log 105=0.2818$

Step-by-step explanation:

Given : If $\log 2=0.3010$, $\log 3=0.4771$ and $\log 7=0.8451$

To find : The value of $\log 105$ ?

Solution :

On factoring the number $105=3\times 5\times 7$

So, we can write expression as

$\log 105=\log(3\times 5\times 7)$

Applying logarithmic property,

$\log (abc)=\log a+\log b+\log c$

$\log 105=\log 3\times \log 5\times\log 7$

We find the value of log 5,

$\log(5)=\log(\frac{10}{2})=\log(10)-\log(2)=1-\log(2)=1-0.3010=0.6990$

Substitute the values,

$\log 105=0.4771\times 0.6990 \times 0.8451$

$\log 105=0.2818$

Therefore, the value is $\log 105=0.2818$

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