Find the value of -

Question

If log 10 base 20+log10 base 30-1/2log 10 base 36

log₁₀20 + log₁₀30 - \(\frac12\) log₁₀36

Answer 1

log₁₀20 + log₁₀30 - \(\frac12\) log₁₀36

 = log₁₀(20 x 30) - log 10\(\sqrt{36}\) (\(\because\) log A + log B = log AB & n log A = log Aⁿ)

= log₁₀600 - log₁₀6

= log₁₀\((\frac{600}6)\)(\(\because\) log A - log B = log \(\frac AB\))

 = log₁₀100

 = log₁₀10²

= 2 log₁₀ 10 (\(\because\) log aⁿ = n log a)

 = 2 (\(\because\) log₁₀10 = 1)

Comments

Nice explaination