Question

write the expression logbsqrt(128/27) in terms of A and C when A=logb2 and C=logb3

Answer 1

use the fact that
\[128=2^7\] and
\[27=3^3\] to rewrite
\[\log(\sqrt{\frac{2^7}{3^3})}\]

Answer 2

then use
\[\sqrt{x}=x^{\frac{1}{2}}\] to rewrite it as
\[\log(\frac{2^7}{3^2})^{\frac{1}{2}}\]

Answer 3

then
\[\frac{1}{2}(\log(2^7)-\log(3^3))\]

Answer 4

then
\[\frac{1}{2}(7\log(2)-3\log(3))\] and finally you have what you want, an expression in
\[\log(2)\text { and } \log(3)\]

Answer 5

so your "final answer" is
\[\frac{1}{2}(7A-3C)\]

Answer 6

hello fred!

Answer 7

when do i get to level 101?

Answer 8

hahaha ur pretty amazing. Always help me.

Answer 9

thank you.

Answer 10

yw, hope steps are clear