Question

If log 2 = 0.301 and log 3 = 0.477, then the value of log 225 is:

Answer 1

log225=2log15=2log(3×5)=2(log3+log5)=2(log3+log10-log2)=2(0.477+1-0.301)=2.358.

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Answer 2

The value is $\log 225=2.352$

Step-by-step explanation:

Given : If log 2 = 0.301 and log 3 = 0.477.

To find : The value of log 225 ?

Solution :

We can write the expression as,

$\log 225=\log (3^2\times 5^2)$

Applying logarithmic property, $\log (ab)=\log a+\log b$

$\log 225=\log (3^2)+\log(5^2)$

Again apply logarithmic property, $\log a^x=x\log a$

$\log 225=2\log (3)+2\log(5)$

$\log 225=2(\log (3)+\log(5))$

Now, the value of log 5 we get by,

$\log 5=\log(\frac{10}{2})=\log 10-\log 2=1-0.301=0.699$

Substitute the values,

$\log 225=2(\log (3)+\log(5))$

$\log 225=2(0.477+0.699)$

$\log 225=2(1.176)$

$\log 225=2.352$

Therefore, the value is $\log 225=2.352$

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