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Conversion of Numbers Using Logarithms

Find the valu...

Question

Find the value of ${log}_{10} 5$ if ${log}_{10} 2 = 0.301$ .

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Solution

We know that: $log a - log b = log \frac{a}{b}$
Hence,
${log}_{10} 5 = {log}_{10} \frac{10}{2} = {log}_{10} 10 - {log}_{10} 2 = 1 - 0.301 = 0.699$

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Similar questions

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,

Find the value of m if a + b = 2c

{l o g}_{10} 2 = 0.3010

{l o g}_{10} 3 = 0.4771

{l o g}_{10} 540 =

{log}_{10} 2 = 0.301

{log}_{10} 11 = 1.041

, then the number of digits in

88^{100}

x = {(0.15)}^{20}

, then find the mantissa of the logarithm of

x

10

{log}_{10} 2 = 0.301

{log}_{3} 10 = 0.477

.

{log}_{10} 2 = 0.3010

{log}_{10} 3 = 0.4771

, then the value of

{log}_{10} (2.25)

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