Question

pl ans this q fast i got a test tomo its urgent please​

Answer 1

Answer:

Step-by-step explanation:

1. Log 216/Log6 = Log x

  => log (216/6) = log x

  => log 36 = log x

 => x = 36.

2. Log (x+y/3) = 1/2(Logx + Logy)

=> 2 Log (x+y/3) = Log x + log y

=>  Log (x+y/3)² = Log xy  (∵ Log a + Log b = Log (ab))

=> (x+y/3)² = xy.

=> x² + y² + 2xy = 9xy

=> x² + y² =  7xy

=> x²/xy + y²/xy = 7

=> x/y + y/x = 7

Hence proved.

3. log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

=>  log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + log₁₀10

=>  log₁₀[5 (5x + 1)] = log₁₀[10(x + 5)]

=>  5(5x + 1) = 10(x + 5)

=>  5x + 1 = 2x + 10

=>  3x = 9

=>  x = 3.