Question

Log10^8+2log10^2-log10^32+log10^5

Answer 1

Answer:

$\large\bold\red{-15}$

Step-by-step explanation:

Given,

$\ log( {10}^{8} ) + 2 \log( {10}^{2} ) - \log( {10}^{32} ) + \ log( {10}^{5} )$

Now,

We know that,

$\bold{\log( {x}^{y} ) = y\ log(x) }$

Therefore,

We get,

$= 8 \log(10) + 2 \times 2\ log(10) - 32 \log(10) + 5\ log(10)$

Further simplifying,

We get,

$= 8 \log(10) + 4\ log(10) - 32\ log(10) + 5 \log(10) \\ = 17\ log(10) - 32 \log(10) \\ = - 15 \log(10)$

Now,

We know that,

$\bold{ \log(10) = 1}$

Putting the value,

We get,

$= - 15 \times 1 \\= - 15$

Hence,

-15 is required Answer.