Question

log5+log(5x+1)=log(x+5)+1​

Answer 1

log 5 + log(5x+1) = log( x+5) +1

log5 + log(5x+1) = log (x+5) + log 10

log ( 5(5x+1)) = log(( ( x+5)10))

compare

5(5x+1) = 10(x+5)

1/2 = x+5)/(5x+1)

Apply Componendo and dividendo

1+2)/(1-2) = x+5 + 5x+1)/(x+5-5x-1)

-3 = 6x +6)/( -4x +4)

-3 = 3/2. ( x+1)/( 1- x)

-2 = ( x+1)/( 1-x)

x+1 = - 2+2x

x= 3

Answer 2

Answer:

Option (B) X = 2

Step by step explanation :

Hey Mate,

Given Equation : log₁₀ 5 + log₁₀ (5X + 1) = log₁₀ (X + 5) + 1

Solution : log ₁₀ 5 + log ₁₀ (5X + 1) = log ₁₀ (X + 5) + 1

=> log ₁₀ 5 + log ₁₀ (5X + 1) = log ₁₀ (X + 5) + log ₁₀ 10

=> log ₁₀ [5 (5X + 1)] = log ₁₀ [10(X + 5)]

=> 5(5X + 1) = 10(X + 5)

=> 25X + 5 = 10X + 50

=> 15X = 45

=> X = 3