Question

If three numbers are in GP, then their logarithm will be in

• A. A.P
• B. G.P
• C. H.P
• D. None of these

Answer 1

Answer: (A), (D)

None of these

Explanation for the correct option:

Finding the relation:

Let, $a,b$ and $c$ are in G.P, then

$b^2=a·c$

By taking $\log$ on both side,

$$\begin{gathered} \log b^2=\log \left(a·c\right) \\ \Rightarrow 2\log b=\log a+\log c\left[\because {\mathrm{loga}}^b=\mathrm{bloga},\log \left(a·b\right)=\mathrm{loga}+\mathrm{logb}\right] \\ \Rightarrow \log b=\frac{\log a+\log c}{2} \end{gathered}$$

If the three terms are in A.P, then the middle term is the arithmetic mean of the other two terms.

So, $\log a,\log b$ and $\log c$ are in A.P

Hence, the correct option is A.