2^(4x-4)=5^(6-4x)?

Question

I know you have to use logs so I get (4x-4)log2 =(6-4x)log5 but then I get stuck. I don't know how to get the x's together. Can someone solve this step by step thanks.

Answer 1

4xlog2 - 4log2 = 6log5 - 4xlog5
x(4log2+4log5) = 4log2+6log5
x = (4log2+6log5)/(4log2+4log5)

Answer 2

ok, to start up you want to get all of your x words on one area of the equation, and all non-x words on the different area. start up like this: 24x + 5 = 12x +40-one Now, flow 12x to the different area. shop in ideas, once you flow a time period to the different area of an equation, you should change its signal. for the reason that 12x is functional, you'll favor to make it unfavourable, like this: 24x - 12x +5 = 40-one Now, flow 5 to the different area replacing its examine to boot, like this: 24x - 12x = 40-one - 5 Now, do the subtraction on each and each area to simplify, like this: 12x = 36 Now divide each and each area through 12 so that you get x and not using a kind in the front of it, like this: x = 3 you're done. problem variety 2: once you've this ------> 3(x + 5) = 4x you should comprehend that the three out the front should be prolonged through both words contained in the parentheses, like this: 3x + 15 = 4x Now, do what you probably did contained in the first problem, flow 3x to the right area. make certain you adjust signs and indicators: 15 = 4x - 3x Simplify: 15 = x done. wish this enables.

Answer 3

the only assistance i can offer (because i really don't feel like doing some math) is that you have to use logs or your knowledge of them to get the 2 and the 5 to be the same number. for example:

2^(3x-5)=8^(x-7)

you must make the 2 equal 8 or vice versa using logarithms. 2^3 equals 8, so sub that in for 8.

2^(3x-5)=2^3(x-7) and then you have 3x-5=3(x-7) and you can solve from there.

Answer 4

log2/log5=(6-4x)/(4x-4)
0.43067(4x-4)=(6-4x)
1.7227x-1.7227=6-4x
5.7227x=7.7227
x=1.3494

Answer 5

2^(4x - 4) = 5^(6 - 4x)
(4x - 4)ln(2) = (6 - 4x)ln(5)
4xln(2) - 4ln(2) = 6ln(5) - 4xln(5)

4xln(2) + 4xln(5) = 6ln(5) + 4ln(2)
x(4ln(2) + 4ln(5)) = 6ln(5) + 4ln(2)
x = (6ln5 + 4ln2)/(4ln2 + 4ln5)
x = (2(3ln5 + 2ln2))/(2(2ln2 + 2ln5))

ANS : (3ln5 + 2ln2)/(2ln2 + 2ln5)

Answer 6

i cant seem to forget about logs but the quadratic equation i did forget. hmm... the second answerer is right, i guess.

Answer 7

you group together the x's
x(4log2+4log5)=6log5+4log2
so:
x=(6log5+4log2)/(4log2+4log5)

Answer 8

sorry i forgot how

Answer 9

(4x-4)Ln2=(6-4x)Ln5
4x-4=(6-4x)(Ln5/Ln2)
4x+(4Ln5/Ln2)x=6Ln5/Ln2+4
x=(6Ln5/Ln2+4)/(4+4Ln5/Ln2)
X=1.349