Question

If 3^( log tan x)+3^( log cot x)=2 then x is -​

Answer 1

It has given that, 3^(log tanx) + 3^(log cotx) = 2

We have to find the value of x.

solution : here 3^(log tanx) + 3^(log cotx) = 2

We know, cotx = 1/tanx

so, log cotx = log (1/tanx) = log(tanx)¯¹ = -log tanx

So, 3^(log tanx) + 3^(-log tanx) = 2

⇒3^(log tanx) + 1/3^(log tanx) = 2

let 3^(log tanx) = p

So, p + 1/p = 2

⇒p² - 2p + 1 = 0

⇒p = 1

So, 3^(log tanx) = 1 = 3^0

⇒log tanx = 0

⇒tanx = 1

x = nπ + π/4

For log to be defined , tanx > 0

So, x = -3π/4, π/4, 5π/4, 9π/4 ...

i.e., x = nπ - 3π/4 , where n is integer.