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.

Step-by-step explanation:

Given;

$\frac{1}{2} log_{10}25 \ - \ 2log_{10}4 \ + \ \ log_{10}32 \ + \ \ log_{10}1$

The above expression is simplified as follows;

$\frac{1}{2} log_{10}25 \ - \ 2log_{10}4 \ + \ \ log_{10}32 \ + \ \ log_{10}1 \\\\= log_{10}25^{\frac{1}{2} } \ - \ log_{10}4^2 \ + \ \ log_{10}32 \ + \ \ log_{10}1\\\\= log_{10} [\frac{25^{\frac{1}{2} } \ \times \ 32 \ \times 1}{4^2} ]\\\\= log _{10}[\frac{5 \ \times \ 32 \ \times \ 1}{16} ]\\\\= log _{10}[5 \ \times \ 2 \ \times \ 1]\\\\=log _{10}[10]\\\\= 1$

Thus, the simplified expression is 1.