Question

The simplified value of 2 log10 5 + log10 8 - ½ log10 4

Answer 1

Answer:

2

Step-by-step explanation:

log 10 5^2+log 10 8-log 10 4^1/2

=log 10 25+log 10 8-log 10 2

=log 10 25*8/2

=log10 100

=2

Answer 2

Given:

• ${\tt{ 2 \ log_{10} 5 + log_{10} \ 8 - \dfrac{1}{2} log_{10} \ 4 }}$

Solution

$\\ \colon\implies{\tt{ 2 \ log_{10} 5 + log_{10} \ 8 - \dfrac{1}{2} log_{10} \ 4 }} \\ \\ \\ \colon\implies{\tt{ log_{10} \ 5^2 + log_{10} \ 2^3 - log_{10} \ 4^{ 1/2 } }} \\ \\ \\ \colon\implies{\tt{ log_{10} \ 25 + 3log_{10} \ 2 - log_{10} \ 2 }} \\ \\ \\ \colon\implies{\tt{ log_{10} \ 25 + 2log_{10} \ 2 }} \\ \\ \\ \colon\implies{\tt{ log_{10} \ 25 + log_{10} \ 4 }} \\ \\ \\ \colon\implies{\tt{ log_{10} \ 25 \times 4 }} \\ \\ \\ {\tt\large\red{Using \ log \ mn = log \ m + log \ n }} \\ \\ \\ \colon\implies{\tt{log_{10} \ 100 }} \\ \\ \\ \colon\implies{\tt{ 2log_{10} \ 10 \: \: \: \: \: \: \: {\tt\large\green{( \dag \: \: \: log_{10} \ 10 = 1 )}} }} \\ \\ \\ \colon\implies{\boxed{\tt\pink{ 2 }}}$

Hence,

• The Value of ${\boxed{\tt{ 2 \ log_{10} 5 + log_{10} \ 8 - \dfrac{1}{2} log_{10} \ 4 }}}$ is 2