Question

please answer fast.......​

Answer 1

First Answer:

log7 log5 (√x + 5) + √x) = 0

⇒ log5 (√x + 5) + √x) = 1 NOTE THIS STEP

⇒ √x + 5 + √x = 5 ⇒ x + 5 = 25 + x - 10√x

⇒ 2 = √x ⇒ x = 4 which satisfies the given equation.

Second Answer:

log3(3^x -8) = 2-x.
=> 3^x - 8 = 3^(2-x)
=> 3^x -8 = 3^2/3^x
=>3^x - 8 = 9/3^x
Let, 3^x = y Therefore, y - 8 = 9/y
=> y^2 - 8y = 9
On solving the above quadratic equation, we get y = 9 and y = -1
=> 3^x = 9 and 3^x = -1
Since, 3^x = -1 is not possible.
Therefore 3^x = 9=> x = 2.
Hence, only solution is x=2

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