Question

solve for x 8^x-8=7^4x

Answer 1

this is a transcendental eq....can't solve it directly....use approximation or numerical methods.

Answer 2

logarithm?

Answer 3

sorry i have to solve it in log form

Answer 4

you could try but theat would not change the transcencdental nature of the equation

Answer 5

is left hand side 8 to the power (x-8) or (8 t0 power x) - 8

Answer 6

Write the exact answer using base-10 logarithms.

or no solution

Answer 7

Is it 8^(x-8)? or 8^x -8

Answer 8

you'd get an x inside the log i.e. as an argument

Answer 9

they are both the same

Answer 10

no...they're not

Answer 11

They aren't.

Answer 12

certianly not same

Answer 13

It would make a big difference if it was 8 to the power x-3

Answer 14

rip:use the equation editor for clarity...

Answer 15

8 to the power of x-3

Answer 16

then 7 to the power 4x

Answer 17

sorry guys =(

Answer 18

oh, ok

Answer 19

\[8^{x-3} = 7^{4x}\] ?

Answer 20

yes!

Answer 21

x = 9log(2)/(3log(2) - log(7))

Answer 22

note you get that by taking a log on both sides

Answer 23

sorry....x = 9log(2)/(3log(2) - 4log(7))

Answer 24

so thats it?

Answer 25

sorry for the earlier trascendental analysis .. I thought that the last x was multiplied by 7^4

Answer 26

yep...hope it was of some help.

Answer 27

thanks!!!!

Answer 28

\[x = -\frac{8 \log{8}}{4 \log{7} - \log{8}} = -2.91637\]

Answer 29

(x-3) ln 8 = 4x ln 7
x-3 / 4x = ln7 / ln 8= 0.93578
x = -1.094

Answer 30

Slight mistake: it's \[3 \log{8} /(\log 8 - 4\log 7)\]
You switched the signs on -4log 7 and log8

Answer 31

Also, this does nothing for her understanding. Here's a more detailed explanation of how to solve this problem:
1) \[8^(x-3)=7^4x\]
2) Insert log functions and carry exponents to left of log expression --> \[(x-3) \log8 = 4x \log 7\]
3) Distribute the terms in the exponents to the log expressions --> \[x \log8 - 3 \log8 = 4x \log7\]
4. Combine like-terms and factor -->\[x(\log8 - 4 \log7) = 3 \log8\]
5. Isolate the variable x --> \[x = 3 \log8/(\log8 - 4 \log 7)\]
6. Solve with calculator... unless you can evaluate logarithmic values in without one...
Answer: -1.09363726

Answer 32

I didn't get it wrong. The original post was 8^(x-8) = 7^(4x)

Answer 33

I wasn't aware that it was changed to three instead of 8

Answer 34

i dont quite see what u mean - i'll plug the results into the original equations

Answer 35

Jimmy Rep, you don't see what the original equation was? It's posted right at the top

Answer 36

I misread. The answer really is -2.916366027
Method is correct, though. Sorry