if 3raised to power x equals 4 raised to power y equals 12 raised to power z then find the value of z?

Question

algebra

Answer 1

Can't be answered without more information.

x = 1, 3^x = 3

3 = 12^z, z = ln(3)/ln(12)

x = 2, 3^x = 9

9 = 12^z, z = ln(9)/ln(12)

etc.

Answer 2

x = y = z = 0

Answer 3

Nice question and you can answer this in many ways and it is easier to write here in logarithmic method.

Given, 3^x = 4^y = 12^z ('^' stands for 'to the power')

Applying logarithms, x log3 = y log4 = z log12

From the above equations, we can write,
x log3 = z log12 & y log4 = z log12

now taking first equation,
x log3 = z { log4 + log3}
log3 {x - z} = z log4 ......... let this be equation P

now taking second equation,
y log4 = z log12
y log4 = z { log4 + log3}
log4 {y - z} = z log3
z log3 = log4 {y - z} ......... let this be equation Q

Divide the equations P and Q, which gives
(x - z) / z = z / (y - z)

Cross Multiply
xy - xz - yz + z^2 = z^2

xy - xz - yz = 0

xy - z(x + y) = 0

xy = z (x + y)

z = xy / (x + y)

Therefore the answer for your question is z = xy / (x + y)

Hope you like this procedure of solving the problem.

Answer 4

The answer is:
z is any real number.

First let's consider this:
3ª is odd for all integer a.
4ª is even for all integer a.
Thus the first part 3ª=4ⁿ; we know that we are not looking for an integer.
Now all we have to do is look for some real number that satisifies the solution. Fortunately, that's all of them. If you give me some 3ª, I can find a real number, n, that makes 12ⁿ equal the number you give me.

Answer 5

the answer will definately be a fraction because the bases are all smaller than 12 but yet they equal each other

Answer 6

3** x = 12 **z
taking log of both sides

x log 3 = z log 12

z= xlog 3/ log 12

similarly
z = y log 4/ log 12

Answer 7

3^x = 4^y = 12^z
z = xlog3/log12
x= ylog4/log3
y anything.

Answer 8

x log3 = z log12 & y log4 = z log12

first equation,
x log3 = z { log4 + log3}
log3 {x - z} = z log4 ......... A

second equation,
y log4 = z log12
y log4 = z { log4 + log3}
log4 {y - z} = z log3
z log3 = log4 {y - z} .........B

Divide the equations A and B which gives
(x - z) / z = z / (y - z)
===>
xy - xz - yz + z^2 = z^2

xy - xz - yz = 0

xy - z(x + y) = 0

xy = z (x + y)

z = xy / (x + y)
I HOPE THAT ANS UR Q