Question

Log(10)z + Log(10)(z+3) = 1

Answer 1

because it is log base 10, take 10 to the power of each side (if it were log base 9, take 9 to the power of each side, if it were ln, take e to the power of each side, etc)\[\log_{10}(z)-\log_{10}(z+3)=1\]
\[10^{\log_{10}(z)-\log_{10}(z+3)}=10^1\]
now the reason we did that is because \[a^{\log_{a}(f(x)}=f(x)\] they cancel out! But notice the left hand side is not just log of a function. you need to use the log laws to simplify it first.\[10^{\log_{10}[z/(z+3)]}=10\]now they cancel and you are left with\[z/(z+3)=10\]\[z=10(z+3)=10z+30\]\[-9z=30\]\[z=-10/3\]