Question

@phi @mathmale

Answer 1

Solve. \[16^{d-4} = 3^{3-d}\]

Answer 2

are you studying logarithms ?

Answer 3

yes

Answer 4

do you know this rule:
\[ \log(a^b) = b\log(a) \]
?
You should first "take the log" of both sides of the equation
then use that rule

Answer 5

on my online classs I cant see the lesson so I come on this site

Answer 6

the first step is "take the log" of both sides.
that means if you have

a = b

take the log means write
log(a) = log(b)

can you do that for your equation (just write in the log)

Answer 7

is 16 the a and 3 the b

Answer 8

a stands for the "entire left side"
b is the right side

Answer 9

16 d−4 is ?
and
3 3−d is b?

Answer 10

yes

Answer 11

ok now what do we do

Answer 12

the idea is if
left_side = right_side
then the log of the left_side equals the log of the right_side
log( left_side ) = log(right_side)

Answer 13

you should now have
\[ \log\left( 16^{d-4}\right) =\log\left( 3^{3-d}\right)
\]

Answer 14

ok I got that now

Answer 15

now use
\[ \log(a^b) = b\log(a) \]
here "b" stands for the entire exponent (no matter how complicated)

use that rule on both sides.
what do you get ?

Answer 16

im not sure can you go through it please

Answer 17

like I saw the work I don't know the answer

Answer 18

It's worth learning how to interpret this rule. Do "pattern matching"
in
\[ \log(a^b) = b\log(a) \]
the "a" matches up with the base
"b" matches with the exponent.
can you match a and b to your problem
\[ \log\left( 16^{d-4}\right) \]

Answer 19

\[ \log\left( 16^{d-4}\right) \] what is that

Answer 20

its confusing me

Answer 21

at the very top you say
***
solve.

\[ 16^{d-4} = 3^{3-d} \]
****

is that what we have to do ?

Answer 22

yea but on my computer it comes up as a bunch of slashes and numbers

Answer 23

what about this

log( 16 ^ (d-4) )

match that to
log( a^b)

what does "a" match up with?
what does "b" match up with ?

Answer 24

that's better

Answer 25

would match up to log16 ^ (d-4) )

Answer 26

we want to use the rule
log( a^b) = a log(b)

Answer 27

can you tell me what the answer is and then tell me how you go it