Question

Is this equation true? please help!

Answer 1

What equation?

Answer 2

\[4\log_{3} x+\frac{ 1 }{ 2 }\log_{3} y-2\log_{3}2=\log_{3}\frac{ x^4\sqrt{y} }{ z^2 } \]

Answer 3

sorry not my area of expertise, so to speak.

Answer 4

Is the 2 before the equal sign supposed to be a z?

Answer 5

These are all of the same base. So remember:

log A + log B - log C

is equal to

log(ABC)

Answer 6

Also, you can move the constants back into the log using:

n log x
= log x^n

Answer 7

yes it´s a z sorry

Answer 8

log(ab/c)*

Answer 9

@CalebBeavers Oh yeah, whoops.

log(AB/C)

Answer 10

Yep, so since that was supposed to be a z then the equation is true.

Answer 11

is bc of the way muntoo explained it?

Answer 12

Yes, so:

\[\Large {4 \log_3 x + {1\over2} \log_3 y -2\log_3 z \\
= \log_3 x^4 + \log_3 \sqrt{y} - \log_3 z^2 \\ = \log_3 ({x^4\sqrt{y}\over z^2}) }\]

Using my rules above.

Answer 13

thanks! what properties did you use to find that out?

Answer 14

In the second line, you move the constants in.
n log x
= log x^n

In the third line, you group the logs together.
log A + log B - log C
= log (AB/C)

Note that we are talking about logs of the same base, in this case, 3.