Compute the following logarithms: $(1$ point each$)$

$($a$)lo{g}_{2}128=7$

$($b$)lo{g}_{3}27=3$

$($c$)lo{g}_{4}64=3$

$($d$)lo{g}_{7}1=0$

Compute the following using modular arithmetic: $(1$ point each$)$

$($a$)42$mod$9$

$($b$)146$mod$23$

$($c$)(5+7)mod10$

$($d$)2^7$mod$11$

Use the Caesar cipher to encrypt the following plaintext: $(4$ points$)$

AGENT COOPER IS IN THE BLACK LODGE

Use the Caesar cipher to decrypt the following ciphertext: $(4$ points$)$

WKH RZOV DUH QRW ZKDW WKHB VHHP

Use the Vigen$$re cipher to encrypt the following plaintext using the key PETE: $(4$

points$)($NOT CHAT GPT$)$

THERE WAS A FISH IN THE PERCOLATOR