Question

is this equation true? and why or why not??

Answer 1

3 log2 x+ 1/2 log2 y - 3 log2 z=log2 [(x^3√y)/(z^3)]

Answer 2

sorry if thats extremely confusing! I have no idea where to start.

Answer 3

\[3 \log_2 x+ \tfrac12 \log_2 y - 3 \log_2 z=\log_2 \left[\frac{x^3√y}{z^3}\right]\]

Answer 4

yea thats it i didnt really know how to put it like that

Answer 5

to start with simplify the Left hand side ; take the constants in front of the logs and make them the powers of the terms in the logs , like this \(n\log_ba=\log_ba^n\)

Answer 6

okay so
log2x^3+log2 y^(1/2)-log2 z^3

Answer 7

thats good !

now use these logarithm properties \[\log_ba+\log_bc=\log_b[ac]\]\[\log_bd-\log_be=\log_b\left[\frac de\right]\]

Answer 8

I have three different logs though.

Answer 9

yes

Answer 10

if we combine those properties , we get

\[\log_bf+\log_bg-\log_bh=\log_b\left[\frac {fg}h\right]\]

Answer 11

okay so is that the simplified version is the left side??

Answer 12

okay wait i got it. i put it all together and got

log2[(x^3*y^.5)/(z^3)

and y^.5 is the same as the square root of y so they are equal! Thanks so much!!!

Answer 13

Yes ! you got it \(\color{red}\checkmark\)