Question

if x,y,z are in GP then log x log y log z are in​

Answer 1

Step-by-step explanation:

if x,y,z are in G.P

then x=a

y=ar

z=ar²

then logx,logy,logz are in G.P

=> log(a),log(ar),log(ar²)

=>loga,(loga+logr),(loga+2logr)

=>from these we can write

=> 2logy=logx+logz

so they are in A.P

Answer 2

If x , y , z are in GP then log x , log y , log z are in arithmetic progression ( AP )

Given : x , y , z are in GP

To find : log x , log y , log z are in

Tip :

1. x , y , z are in GP then y² = xz

2. x , y , z are in AP then 2y = x + z

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that x , y , z are in GP

Step 2 of 2 :

Find the result

Since x , y , z are in GP

y² = xz

Taking logarithm in both sides we get

$\sf log \: {y}^{2} = log \: (xz)$

$\sf \implies \: 2log \: y = log \:x + log \: z$

So log x , log y , log z are in arithmetic progression ( AP )

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