Logarithmic Equation

Question

log(1-y) + log(4-y) = log(18-10y)

Answer 1

Hi Ethan,

 

We can use the product rule of logarithms to write the left hand side as below

log(1-y)(4-y) = log(18-10y)

Since the bases are the same on both sides, then the values are equal to each other

(1-y)(4-y) = 18-10y

 

If we solve for y, we get y=-7 and y=2

 

Since logs can not be less than or equal to 0, only y=-7 will satisfy the equality.