Question

solve for the unknow for this equation. 8^z+1=32sqrt2

Answer 1

write it properly

Answer 2

\[8^{z+1}=32\sqrt{2}\]

Answer 3

\[8^{z+1} = 32 \times \sqrt{2}\]
\[2^{3 \times (z+1)} = 2^{5} \times 2^{\frac{1}{2}}\]
\[2^{ 3z+3} = 2^{5+ \frac{1}{2}} \]
Both sides base is common so

\[{ 3z+3} = {5+ \frac{1}{2}} \]
6z + 6 = 10 + 1
6z = 11-6

\[z = \frac{5}{6} \]

Answer 4

thanks

Answer 5

let me process how you did this

Answer 6

is there a formula I need to understand for this?