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

Question

The value of the expression ( log 10 2)3+ log 10 8 ⋅ log 10 5+( log 10 5)3 is (A) rational which is less than 1 (B) rational which is greater than 1 (C) equal to 1 (D) an irrational number

Tardigrade Admin · Accepted Answer

log 10 2=a and log 10 5=b ⇒ a+b=1 ; a3+3 a b+b3=? Now .(a+b)3=1 ⇒ a3+b3+3 a b=1 ⇒(C)

Q. The value of the expression $(lo g_{10} 2)^{3} + lo g_{10} 8 \cdot lo g_{10} 5 + (lo g_{10} 5)^{3}$ is

rational which is less than 1

rational which is greater than 1

equal to 1

an irrational number

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

Q. The value of the expression (log10​2)3+log10​8⋅log10​5+(log10​5)3 is