Question

Hello everyone ,.
I have a question for ull
I'll mark the answer as brainliest.
So plz solve question 24

Answer 1

(24)

$Given : 5^{log x} + 3^{log x} = 3^{log x + 1} - 5^{log x - 1}$

Let log x = a.

= > 5^a + 3^a = 3^(a + 1) - 5^(a - 1)

= > 5^a + 5^(a - 1) = 3^(a + 1) - 3^(a)

We know that a^(m - n) = a^m * a^n

= > 5^a + 5^a * 5^-1 = 3^a * 3^1 - 3^a

= > 5^a(1 + 1/5) = 3^a(3 - 1)

= > 5^a(6/5) = 3^a(2)

= > 5^a/3^a = 10/6

= > (5/3)^a = (5/3)^1

= > a = 1.

So,

= > log x = 1

= > log x = log 10

= > x = 10.

Hope this helps!