Using log tables, evaluate √ {(2.3)^5 + (0.537)^3/(72.5)^4-(18.25)^2}.

Question

Using log tables, evaluate \(\sqrt{\cfrac{(2.3)^5+(0.537)^3}{(72.5)^4-(18.25)^2}}.\)

√ {(2.3)⁵ + (0.537)³/(72.5)⁴-(18.25)²}

Answer 1

Let x = \(\sqrt{\cfrac{(2.3)^5+(0.537)^3}{(72.5)^4-(18.25)^2}}\)

Let a = (2.3)⁵

Taking log on both sides, we get 

log₁₀ a = 5.log₁₀ (2.3)

\(\therefore\) log₁₀ a = 5 (0.3617) = 1.8085

\(\therefore\) a = antilog (1.8085) = 6.434 \(\times\) 10¹ = 64.34

b = (0.537)³

Taking log on both sides, we get

log₁₀ b = 3.log₁₀ (0.537) = 3(\(\bar1\).7300)