Question

find the value of log 32 to the base 10,if log 2=0.3010​

Answer 1

Given:-

• $\sf log_{10}(2) = 0.3010$

To find:-

• $\sf log_{10}(32)$

Answer:-

Given that, $\sf log_{10}(2) = 0.3010,$ we have to find the value of $\sf log_{10}(32).$

We know that,

$\sf 32 = 2 \times 2 \times 2\times 2\times 2$

$\longrightarrow \sf 32 = 2^5$

So,

$\sf log_{10}(32) = log_{10}(2^5)$

Now we have to use a property,

$\dag \large \underline{ \boxed{ \bf{ \orange{ log_{b}( {a}^{c} ) = c log_{b}(a) }}}}$

$\sf \longrightarrow log_{10}(32) = 5\times log_{10}(2)$

And it is given that, $\sf log_{10}(2) = 0.3010.$ So putting this value, we get,

$\sf \longrightarrow log_{10}(32) = 5\times 0.3010$

$\sf\longrightarrow log_{10}(32) = 1.505$

Thus, the required answer is,

$\longrightarrow \underline{\underline{\sf{\green{log_{10}(32) = 1.505}}}}$