Question

Solve the equations using properties of logs:
a.) 3log[11](x) = 2log[11]8 b.) 2log[5](x) = 3log[5]9

Answer 1

\[3\log_{11}(x)=2\log_{11}8 \]

Answer 2

From properties of logs\[3\log_{11}x=\log_{11}x^3\]and\[2\log_{11}8=\log_{11}8^2=\log_{11}64\]so the first equation boils down to\[\log_{11}x^3=\log_{11}64 \rightarrow x^3=64\]so that\[x=4\]

Answer 3

\[B.) 2\log_{5}(x)=3\log_{5}9 \]

Answer 4

It's something similar for the second one too.

Answer 5

is B.) up there too?

Answer 6

?

Answer 7

there were two equations i posted, A and B

Answer 8

\[x^2=9^3=729 \rightarrow x=\pm 27\]

Answer 9

Yeah, I know, but the procedure is the same. The bases are different but it's irrelevant. It's just something to throw you off. As long as the bases are the same in your equation, you can remove the logs in the end using the definition of the log.

Answer 10

So the answer for B.) is + or - 27?

Answer 11

yes

Answer 12

where did the 729 come from?

Answer 13

9^3?

Answer 14

729 is 9^3