Express the following as a single logarithm :

$1 − \dfrac{1}{3} \log_{10} \space 64$

Given,

$\Rightarrow 1 - \dfrac{1}{3} \log${10} 64 \\[1em] \Rightarrow \log{10} 10 − \log{10} 64^{\dfrac{1}{3}} \\[1em] \Rightarrow \log{10} 10 − \log{10} \sqrt[3]{64} \\[1em] \Rightarrow \log{10} 10 − \log{10} 4 \\[1em] \Rightarrow \log{10} \dfrac{10}{4} \\[1em] \Rightarrow \log{10} \dfrac{5}{2} \\[1em] \Rightarrow \log{10} \space 2.5

Hence, $1 − \dfrac{1}{3} \log_{10} 64$ = log₁₀ 2.5