3x = 28 (4x) . . . How do I solve for x?

Question

The equation is stated as follows:

3 raised to x is equal to 28 times 4 raised to x.

Please help me on this... What's the solution for this equation?

Answer 1

take the log of both sides of the equation
you then get log(3)*X=log(28)+log(4)*X
The solution is then only dependent on the quality of the log tables you have available.

Answer 2

3^x = 28*(4^x)

First, divide both sides by 4^x, to get

(3^x)/(4^x) = 28

Note that we can change the left hand side to a fraction with an exponent.

(3/4)^x = 28

And now, we can convert this to logarithmic form. The base is odd, being a fraction, but it's still a base.

log [base 3/4](28) = x

If you wanted to calculate an approximate value, all you'd have to do is use the change of base formula.

Either calculate log (28) / log (3/4),
OR ln(28) / ln(3/4)

Answer 3

hii, ur question will be solved using logarithms,
i.e ur question is 3^x = 28*4^x
taking x terms on one side:
3^x/4^x = 28
or (3/4)^x = 28
taking log:
x log(3/4) = log28
or x = log28/log(3/4).
i dont have calculator now, so u can take log and fing the value of x.

Answer 4

It seems that u guys have too much access to internet and don't apply your mind to solve the problem and just post it here for other people to answer. In my country even a person who ever in his entire life has read log will answer you. Bye (brain power increases when it is put to work)

Answer 5

Its easy!


Silly way : We take it as told in the statement :
(x-3) = 28 (x-4)
=> x = 112 / 25/
=> x = 4.48
Solve it.


Now,
a more logical way to see is 3^x = 28(4^x)
take log on both sides and tada!
=>xlog(3) = log28 + xlog(4)
=> x = [log28 / {(log(3)-log(4)}]
=> x = 1.44/(0.4771-0.6020)
=> x = - (1.44/0.1249)
=> x = -11.529223378702962369895916733387



Peace out.

Answer 6

3^x = 28 * 4^x

Take logs of both sides

x log 3 = log (28 * 4^x)

x log 3 = log 28 + x log 4

x (log 3-log 4) = log 28

x = log 28 / (log 3 - log 4)

= log 28 / log (3/4) = -11.6 (3sf)

Answer 7

if u wrote out the equation correctly then x=0 (zero) but what the heck does 3 RAISED to x mean?? it might not mean (3x)

Answer 8

3 raised to x is equal to 28 times 4 raised to x.
Take log of both sides. You get
x log3 =log28 + x log4
i.e.,
x (log3 -log4) = log28
i.e.,
x = log28 / (log3 - log4)
= 1.447/(0.4771- 0.6020)
= 1.447/ (- 0.1249)
= - 11.585

Answer 9

equation is wrong..lowest x can be is 0 for which the equation is false..all other values it will be false

Answer 10

3x = 24*4x
3x = 96x
96/3 = x*x
32 = x*x
square root of 32 = x*x
5.65 = x
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