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  4. The value of the expression ( log 10 2)3+ log 10 8 ⋅ log 10 5+( log 10 5)3 is

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Q. The value of the expression $\left(\log _{10} 2\right)^3+\log _{10} 8 \cdot \log _{10} 5+\left(\log _{10} 5\right)^3$ is

Continuity and Differentiability

Solution:

$\log _{10} 2=a$ and $\log _{10} 5=b \Rightarrow a+b=1 ; a^3+3 a b+b^3=?$
Now $.(a+b)^3=1 \Rightarrow a^3+b^3+3 a b=1 \Rightarrow(C)$