Express as an equivalent expression, using the individual logarithms of w,x,y and z. log a (xy^2z-3)
well, loga (zt^2/q^3)=loga (z)+ 2loga(t)-3loga(q)
see if you can take it from there.
3logx+2logy-3logq
To express the expression logᵃ(xy²z - 3) in terms of individual logarithms of w, x, y, and z, we can break down the expression using the properties of logarithms.
First, let's deal with the constant term -3.
logᵃ(-3) = logᵃ(3)
Now, let's split the exponential term xy²z into individual logarithms.
logᵃ(xy²z) = logᵃ(x) + logᵃ(y²) + logᵃ(z)
Using the power rule of logarithms, we can rewrite the term logᵃ(y²):
logᵃ(y²) = 2logᵃ(y)
Putting it all together, the equivalent expression in terms of individual logarithms of w, x, y, and z is:
logᵃ(3) + logᵃ(x) + 2logᵃ(y) + logᵃ(z)