Question 380916
that expression would be shown as:


log(b,(2y+5)) - 4*log(b,(y+3))


in general x * log(y) = log(y^x)


your expression becomes:


log(b,(2y+5)) - log(b,((y+3)^4))


in general log(x) - log(y) = log(x/y)


your expression becomes:


log(b,((2y+5)/(y+3)^4))


to show you how this works, we will let b = 10 because your calculator can do logs to the base of 10 (usually called the LOG function).


we will let y = 5 (chosen at random small enough to calculate easily).


your original expression becomes:


log(2y+5) - 4*log(y+3)


the base of 10 is implied.


substituting 5 for y, we get:


log(2*5+5) - 4*log(5+3) which becomes:


log(15) - 4*log(8) which becomes -2.436268689


looking at our final expression of:


log(b,(2y+5)/(y+3)^4), we get:


log((2y+5)/(y+3)^4).


the base of 10 is implied.


substituting 5 for y, we get:


log(15/8^4) which becomes log(15/4096).


using our calculator, we get log(15/4096) = log(.003662109) which equals -2.436268689


we get the same answer either way, so the translation is good, and the answer to your question is:


log(b,2y+5) - 4*log(b,y+3) = log(b,(2y+5)/(y+3)^4)  which looks like:


{{{log(b,(2y+5)) - 4*log(b,(y+3)) = log(b,((2y+5)/(y+3)^4))}}}