Question

If $x=\log_{5}7, y=\log_{7}27, z=\log_{3}5$, show that xyz = 3.

Answer 1

Answer:

Step-by-step explanation:

Hi,

Here we will be using the following properties of  

logarithm:  

logₐb = log b/log a  

nlog a = log aⁿ  

Given that x = log₅7,

which we can write as

x = log 7/log 5

Given y = log₇27

which we can rewrite as

y = log 27/log 7

But log 27 = log 3³ = 3 log 3

So, y = 3 log 3/log 7

Given z = log₃5

We can rewrite z as log 5/log 3

Consider xyz

= (log 7/log 5)*(3log 3/log 7)*(log 5/log 3)

= 3

= R.H.S

Hope, it helps !