Answer :
Solution:
Given the expression;
[tex]5\log_(2+\log_(3[/tex]Following addition and power property of logarithm;
[tex]\begin{gathered} a\log_b=\log_b^a \\ \\ \log_a+\log_b=\log_ab \end{gathered}[/tex]Thus;
[tex]\begin{gathered} 5\log_{10}2+\log_{10}3=\log_{10}2^5+\log_{10}3 \\ \\ 5\log_{10}2+\log_{10}3=\log_{10}32+\log_{10}3 \\ \\ 5\log_{10}2+\log_{10}3=\log_{10}(32\times3) \\ \\ 5\log_{10}2+\log_{10}3=\log_{10}96 \end{gathered}[/tex]ANSWER:
[tex]\log_{10}96[/tex]