CAT 2017 Logarithms Question (Medium)

Question

If is the arithmetic mean of , , and , then equals TITA .

Accepted Answer

Step 1 Let the three expressions be - - - Take their arithmetic mean Step 2 Use log rules , and Now expand - First term - Second term - Third term Add - terms - terms - terms Total sum Divide by 3 This means , , --- Final Answer

CAT 2017

Quantitative

Logarithms

Medium

If $\log(2^a \times 3^b \times 5^c)$ is the arithmetic mean of $\log(2^2 \times 3^3 \times 5)$ , $\log(2^6 \times 3 \times 5^7)$ , and $\log(2 \times 3^2 \times 5^4)$ , then $a$ equals (TITA).

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