Question

Solve 4^(2x) = 7^(x−1).

Answer 1

@phi

Answer 2

are you studying logarithms ?

Answer 3

@phi yes

Answer 4

have you learned how to "take the log" of both sides ?

Answer 5

no @phi

Answer 6

"take the log" means write log in front of a number (or expression)

for example, to take the log of 10 you write
log 10

Answer 7

oh ok so, 4 would be log 4

Answer 8

so log of 4 is log 4

write down your equation after you "take the log" of both sides
(don't simplify anything, just write log on each side)

Answer 9

ok so I have: log 4^(2x)= log 7 ^(x-1)

Answer 10

yes, and technically we should put in parens because we are doing
\[ \log\left( 4^{2x}\right) = \log\left(7^{(x-1)} \right)\]

Answer 11

oh ok, got it! Now what?

Answer 12

there is a "property" of logarithms that we now use (this is the reason we are using logs)

the property is
\[ \log(a^b) = b \log(a) \]

Answer 13

ok!

Answer 14

any idea how to use that property on both sides of your equation?
for example, if you apply it to the left side, what do you get ?

Answer 15

on the left side I will have: Log (4^2)=^2log(4) ?

Answer 16

you mean
\[ \log(4^2) = 2 \log(4) \]
but you don't have 4^2 you have 4^(2x)

Answer 17

try again

Answer 18

yes

Answer 19

so log(4^2) = 2log(4)

Answer 20

i put it in my calculator and I got 1

Answer 21

so would 1 be the answer

Answer 22

these are my answer choices:
2.35389
−2.35389
−1
1

Answer 23

no. we'll get back to using the calculator later.

but the left side is
\[ \log(4^{2x} ) \]

Answer 24

ok!

Answer 25

use the rule on that

Answer 26

how would I use the rule for log (4^2x)? Would I do: log (4*2)=2log(4)
log(ab)=blog(a)

Answer 27

a= 4 and b=2

Answer 28

the idea is to "match up" your problem with the rule