Question

can someone help me with this problem?
"use the change of base formula to evaluate each expression. Then convert it to a logarithm in base 8":
log(base2)9

Answer 1

i got \[\log_{8} 729\]
is that correct?

Answer 2

hi

Answer 3

use the formula log(base b)x=log(base a)x/log(base a)b
log(base2)9=log(base8)9/log(base8)2, now you can still simplify this by dividing them

Answer 4

Let \(k = log_2{9} \implies 2^k = 9\)
\[ \implies log_8 (2^k) = log_8 9\]
\[ \implies k\ log_8 2 = log_8 9\]
\[ \implies k = \frac{log_8 9}{log_8 2}\]
\[ \implies log_2 9 = \frac{log_8 9}{log_8 2}\]