assuming you mean
[tex]log_2(t^3-1)=-3[/tex]
remember
[tex]log_a(b)=c[/tex] translates to [tex]a^c=b[/tex]
translate
[tex]log_2(t^3-1)=-3[/tex] translates to [tex]2^{-3}=t^3-1[/tex]
[tex] \frac{1}{2^3} =t^3-1[/tex]
[tex] \frac{1}{8} =t^3-1[/tex]
add 1 to both sides
[tex] \frac{9}{8} =t^3[/tex]
cube root both sides
[tex] \frac{ \sqrt[3]{9} }{2}=t[/tex]
