Difficulty in subtracting two different bases of log and simplifying it.

[Kolby]

I am stuck because as far as I know you need a perfect square number to simplify with a different base. For example I take log4 6 and change it to form log2, the formula would become log2 6/log2 4

The denominator would then become 2 because 2 square = 4 but in this question the number for the denominator is not a perfect square which makes it no sense at all :|

https://imagizer.imageshack.us/v2/800x600q50/593/u4dr.jpg

 

[Deleted member 4993]

I am stuck because as far as I know you need a perfect square number to simplify with a different base. For example I take log4 6 and change it to form log2, the formula would become log2 6/log2 4

The denominator would then become 2 because 2 square = 4 but in this question the number for the denominator is not a perfect square which makes it no sense at all :|

https://imagizer.imageshack.us/v2/800x600q50/593/u4dr.jpg

First use the fact that log₄16 = 2
because 4² = 16

then

log₅(8y-6) - log₅(y-5) = log₄16

log₅[(8y-6)/(y-5)] = 2

Now use definition of log_a(b) = c → a^c = b and continue.....