Question

Solve 4x + 7 = 6x - 1

Answer 1

Subract 7 both sides
4x + 7 = 6x - 1
-7 -7
==========
4x=6x-8
4x-6x=8
-2x=8
x=8/-2
x=-4

Answer 2

sorry i couldnt do eqn in original. its actually: \[4^{x+7} = 6^{x-1}\]

Answer 3

Get the log of both sides. It's the only way...

Answer 4

so log(x+7) 4 = log(x-1) 6?

Answer 5

Let's use natural logarithm.
\[\Large \ln(4^{x+7}) = \ln (6^{x-1})\]

Answer 6

Hmm?
Use this property
\[\Large \ln b^p = p\ln (b)\]and the fact that ln(4) and ln(6) are just constants.

Answer 7

how do i enter that into my calculator?

Answer 8

Not yet. You still have to solve.

Answer 9

By isolating x.

Answer 10

so get x on one side?

Answer 11

Yup. But you still have to deal with these:\[\Large \ln(4^{x+7}) = \ln (6^{x-1})\]
and use that property I posted.

Answer 12

im not sure how

Answer 13

The exponent just becomes a factor...
\[\Huge \ln b^{\color{red}p}= \color{red}p\ln(b)\]

Answer 14

so it would become ln(4^[x+7]) =(x-1)ln(6)?

Answer 15

Yes... partly, but you should do the same to the left side :P

Answer 16

oh i thought it was like how the equation was set up, sorry about that so (x+7)ln(4)=(x-1)ln(6)?

Answer 17

Yup.
And after a bit of algebraic manipulation, you get
\[\Large \frac{x+7}{x-1}=\frac{\ln 6}{\ln 4}\]
\[\Large \frac{x+7}{x-1}=\color{blue}{\log_46}\]
and that part in blue is just a constant you can enter into your calculator (if not, then just divide ln 6 by ln 4)

Answer 18

so x+7/x-1 =~ 1.8

Answer 19

yes, and just solve normally.

Answer 20

I don't know what log(base4) of 6 is so I'll just leave it as k for now.
You have the calculator, you know what it is
\[\Large x+7 = \color{blue}k(x-1)\]
And this is just your basic linear equation :P
Solve as you see fit XD

Answer 21

x+7~1.8(x-1)
x+7~1.8x-1.8
-.8x~5.2
x~-6.5 is what i got?

Answer 22

Nope.
You subtracted 7 from 1.8x
They're not similar terms.
Never forget your basics.