Simplify:
${log}_{10} 5 + 2 {log}_{10} 4$

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Solution

${log}_{10} 5 + 2 {log}_{10} 4$
$= {log}_{10} 5 + {log}_{10} 4^{2}$
$= {log}_{10} 5 + {log}_{10} 16$
$= {log}_{10} 80$ [Using product rule of logarithm]
$= {log}_{10} (10 \times 8)$
$= {log}_{10} 10 + {log}_{10} 8$
$= 1 + {log}_{10} 8$

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2 {log}_{10} 5 + {log}_{10} 5 - \frac{1}{2} {log}_{10} 4

2 {log}_{10} 5 + {log}_{10} 8 - \frac{1}{2} {log}_{10} 4

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{log}_{10} 5 + {log}_{10} 8 - 2 {log}_{10} 2

a = 1 + l o g_{10} 2 - l o g_{10} 5, b = 2 l o g_{10} 3

c = l o g_{10} m - l o g_{10} 5,

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