Question

given that t = log 8 x, find each of the following in terms of t
find: log 4 2x

Answer 1

\[\large t = \log_8 x\]this?

Answer 2

yes

Answer 3

You know the change of base formula?

Answer 4

no, i just started to learn this topic

Answer 5

Okay, until further notice, accept this formula... say you have a log
\[\large \log_b M\] And you want to change the base to a new one, say, a.
then
\[\large \log_bM= \frac{\log_aM}{\log_ab}\]

Answer 6

okay, i get it

Answer 7

Well, you have
\[\huge t = \log_8x \]
Change the base to 4 instead, following that formula I gave you.

Answer 8

okay.... done

Answer 9

What did you get?

Answer 10

\[\log _{4} x \over \log _{4} 8\]
is that it?

Answer 11

Very good.
\[\huge t = \frac{\log_4 x}{\log_4 8}\]

You'd do well to remember that \(\large \log_48\) is just a constant... which can be multiplied to both sides to get...?

Answer 12

I don't understand

Answer 13

Multiply \(\large \log_4 8 \) on both sides.

Answer 14

multiply with which one?

Answer 15

on both sides of this equation
\[\huge t = \frac{\log_4 x}{\log_4 8}\]

Answer 16

i don't know how to multiply it. sorry, but can u tell me. ..

Answer 17

\[\huge t\times \color{red}{\log_48} = \frac{\log_4 x}{\log_4 8}\times\color{red}{\log_4 8}\]

Answer 18

oh, now I get it!

Answer 19

That is good. Can you continue?

Answer 20

\[t×\log _{4}8=\log _{4} x\]

Answer 21

Good. And now, you have expressed \(\large \log_4 x\) in terms of t.
You can do away with that \(\times\) sign

Answer 22

\[t \log _{4}8=\log _{4} x\]

Answer 23

still not understand with this