Write the log as a single function: logx + 2logy - logz
n * log ( a ) = log ( a ^ n )
log ( a ) + log ( b ) = log ( a * b )
log ( a ) - log ( b ) = log ( a / b )
2 * log ( y ) = log ( x ^ 2 )
log( x ) + 2 * log ( y ) - log ( z ) =
log ( x * y ^ 2 / z )
To write the expression logx + 2logy - logz as a single logarithmic function, we'll need to use some logarithmic properties. Recall that we can combine logarithms using the rules:
1. loga + logb = log(ab)
2. loga - logb = log(a/b)
3. c * loga = loga^c
Using these properties, here's how we can simplify the expression:
logx + 2logy - logz
Now, let's simplify each term step by step:
1) logx + logy^2 - logz (Using property 3: c * loga = loga^c)
2) log(xy^2) - logz (Using property 1: loga + logb = log(ab))
Now we have log(xy^2) - logz. These two terms can be combined further by using the property 2:
3) log((xy^2)/z) (Using property 2: loga - logb = log(a/b))
So, the single logarithmic function equivalent to logx + 2logy - logz is log((xy^2)/z).