Question

Given that log3(z - 1) - logz z = 1+ 3 log3 y, express z in terms of y.

Answer 1

z = 1 + 9y³

Explanation:

It looks like you have ...

`\log_3{(z-1)}-\log_z{(z)}=1+3\log_3{(y)}\\\\\log_3{(z-1)}-1=1+\log_3{(y^3)}\\\\\log_3{(z-1)}=2+\log_3{(y^3)}\qquad\text{add 1}\\\\z-1=(3^2)(y^3)\qquad\text{take antilog}\\\\\boxed{z=1+9y^3}\qquad\text{add 1}`