- anonymous

Solve 4^(2x) = 7^(x−1).

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

- freckles

have you tried taking ln( ) of both sides

- anonymous

wouldn't it be log?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- freckles

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

- freckles

not distribute on the right hand side

- freckles

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

- anonymous

1.38629436112(2x) I mean, sorry :)

- freckles

are you allowed to approximate ?

- anonymous

no, not until we have the final answer

- freckles

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

- freckles

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

- anonymous

1.94591014906

- anonymous

1.94591014906x-1.94591014906

- freckles

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

- anonymous

oh yes! Sorry

- freckles

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

- freckles

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

- freckles

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

- freckles

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

- anonymous

2.77258872224x=1.94591014906x-1.94591014906

- freckles

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

- anonymous

i didn't :)

- freckles

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

- anonymous

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

- freckles

your calculator can only show you so many digits

- freckles

it doesn't have an infinite screen display

- freckles

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)

- anonymous

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

- freckles

|dw:1438798478614:dw|

- freckles

\[\ln(4^{2x})=\ln(7^{x-1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x-1) \ln(7) \\ 2 \ln(4) x=\ln(7) x- \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x -\ln(7) x=-\ln(7) \\ ( 2 \ln(4)-\ln(7) )x=-\ln(7)\]
I'm going to leave the last step to you

- anonymous

Alright, so I got 2 In (-3) =-In(7)
In(-3)^2=-In(7)
yes?

- anonymous

2.35389<---is my answer

- anonymous

yes?

- anonymous

I gotta go eat lunch:) Please message me if I was wrong

- freckles

not sure where you got 2 ln(-3)=-ln(7)
just divide both sides by what x is being multiplied by
which is 2ln(4)-ln(7)
this does not equal 2 ln(-3)
divide both sides by 2ln(4)-ln(7)

- freckles

\[\ln(4^{2x})=\ln(7^{x-1}) \\ \\ \text{ Now use power rule } \\ 2x \ln(4)=(x-1) \ln(7) \\ 2 \ln(4) x=\ln(7) x- \ln(7) \\ \text{ the step I was asking you \to do is subtract } \ln(7) x \text{ on both sides } \\ 2 \ln(4) x -\ln(7) x=-\ln(7) \\ ( 2 \ln(4)-\ln(7) )x=-\ln(7) \\ x=\frac{-\ln(7)}{2 \ln(4)-\ln(7)}\]

- anonymous

-3.29?

- freckles

http://www.wolframalpha.com/input/?i=-ln%287%29%2F%282ln%284%29-ln%287%29%29
this calculator says that is approximately -2.35

Looking for something else?

Not the answer you are looking for? Search for more explanations.