Question

1/2 log base 10 raise to 25 - 2 log base10 raise to 4 +log base 10 raise to 32 + log base 10 raise to 1

Answer 1

Complete question:

Simplify 1/2 log base 10 raise to 25 - 2 log base10 raise to 4 +log base 10 raise to 32 + log base 10 raise to 1

Answer:

the simplified expression is 1.

Explanation:

Given;

`(1)/(2) log_(10)25 \ - \ 2log_(10)4 \ + \ \ log_(10)32 \ + \ \ log_(10)1`

The above expression is simplified as follows;

`(1)/(2) log_(10)25 \ - \ 2log_(10)4 \ + \ \ log_(10)32 \ + \ \ log_(10)1 \\\\= log_(10)25^{(1)/(2) } \ - \ log_(10)4^2 \ + \ \ log_(10)32 \ + \ \ log_(10)1\\\\= log_(10) [\frac{25^{(1)/(2) } \ * \ 32 \ * 1}{4^2} ]\\\\= log _(10)[(5 \ * \ 32 \ * \ 1)/(16) ]\\\\= log _(10)[5 \ * \ 2 \ * \ 1]\\\\=log _(10)[10]\\\\= 1`

Thus, the simplified expression is 1.