To simplify the given expression, we can use logarithmic rules to combine the terms:
1/2log(z+1) - 2log(x) - 4log(y) - 3log(z)
Using the laws of logarithms:
1/2log(z+1) - log(x^2) - log(y^4) - log(z^3)
Now, applying the power rule of logarithms:
log(sqrt(z+1)) - log(x^2) - log(y^4) - log(z^3)
Combining the logarithmic terms:
log[(sqrt(z+1) / (x^2 y^4 z^3))]
Therefore, the simplified expression for 1/2log(z+1) - 2logx - 4logy - 3logz is:
To simplify the given expression, we can use logarithmic rules to combine the terms:
1/2log(z+1) - 2log(x) - 4log(y) - 3log(z)
Using the laws of logarithms:
1/2log(z+1) - log(x^2) - log(y^4) - log(z^3)
Now, applying the power rule of logarithms:
log(sqrt(z+1)) - log(x^2) - log(y^4) - log(z^3)
Combining the logarithmic terms:
log[(sqrt(z+1) / (x^2 y^4 z^3))]
Therefore, the simplified expression for 1/2log(z+1) - 2logx - 4logy - 3logz is:
log[(sqrt(z+1) / (x^2 y^4 z^3))]