Question

Solve 4^(2x) = 7^(x−1).

Answer 1

@Astrophysics @rishavraj @ganeshie8

Answer 2

have you tried taking ln( ) of both sides

Answer 3

wouldn't it be log?

Answer 4

\[\ln(4^{2x})=\ln(7^{x-1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x-1) \ln(7)\]
you can use log too if you want

Answer 5

not distribute on the right hand side

Answer 6

and put your terms with x in it on one side and your terms without x on the opposing side

Answer 7

1.38629436112(2x) I mean, sorry :)

Answer 8

are you allowed to approximate ?

Answer 9

no, not until we have the final answer

Answer 10

ok so leave that one side as 2ln(4)x
and distribute on the other side
recall the distributive property is a(b+c)=ab+ac

Answer 11

use distributive property here and what do you get:
\[\ln(7)(x-1)=?\]

Answer 12

1.94591014906

Answer 13

1.94591014906x-1.94591014906

Answer 14

I think you mean to say ln(7)x-ln(7)

Answer 15

oh yes! Sorry

Answer 16

\[\ln(4^{2x})=\ln(7^{x-1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x-1) \ln(7) \\ 2 \ln(4) x=\ln(7) x- \ln(7) \]

Answer 17

now to get the x people together
subtract ln(7)x on both sides

Answer 18

\[ax=bx-c \\ ax-bx=-c \\ x(a-b)=-c \\ \text{ the last step is to choose to divide by } \\ \text{ what is in front of the } x \\ \\ \text{ in this example that would be } (a-b) \\ x=\frac{-c}{a-b}\]

Answer 19

this is exactly what you are going to do here
first subtract ln(7)x on both sides
then use my example as a guide sorta to finally find x

Answer 20

2.77258872224x=1.94591014906x-1.94591014906

Answer 21

I thought you aren't allowed to approximate until you have final answer

Answer 22

i didn't :)

Answer 23

ln(7) is irrational
there is no way you can write out the whole number
same for ln(4)

Answer 24

oh. Sorry, I just typed it into my calculator & thats what it said

Answer 25

your calculator can only show you so many digits

Answer 26

it doesn't have an infinite screen display

Answer 27

anyways...
\[\ln(4^{2x})=\ln(7^{x-1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x-1) \ln(7) \\ 2 \ln(4) x=\ln(7) x- \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x -\ln(7) x=-\ln(7)\]
try factoring the x out on the left hand side like I did in my example
ax-bx=x(a-b)

Answer 28

2 In(x)-In(-3)x=-In (7)