Question

if logb^2 = x and logb^3 = y, evaluate x and y
logb432
logb648
logb 4/?9
logb81/logb^2

Answer 1

is this
\[\log_b(2)=x,\log_b(3)=y\]?

Answer 2

yes

Answer 3

yes

Answer 4

use
\[432=2^43^3\] to get
\[\log_b(432)=\log_b(2^4\times3^3)=\log_b(2^4)+\log_b(3^3)=4\log_b(2)+3\log_b(3)\]
\[4x+3y\] a problem only a math teacher could love.
others are similar

Answer 5

by which i mean write the input in terms of powers and multiples of 2 and 3, then break the log apart as above

Answer 6

ok

Answer 7

can you help me out with the rest especially logb 4/9 and logb8^1/logb^2

Answer 8

\[\frac{4}{9}=\frac{2^2}{3^2}\] so
\[\log(\frac{4}{9})=\log(\frac{2^2}{3^2})=\log(2^2)-\log(3^2)=2\log(2)-2\log(3)=2x-2y\]

Answer 9

ok