Question

What is the value of x^4 + y^4 if 4^x = 64 and 6^y = 36?​

Answer 1

Given

We have given 4ˣ= 64 and 6ʸ= 36

To Find

We have to find the value of x⁴+y⁴

How to solve ?

We will use the laws of exponential and powers and hence solve the given Question.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Concept:

If bases are same with unlike powers on both the sides then it best automatically cancelled.

4ˣ= 64 and 6ʸ= 36

64 can also be written as 4×4×4 or 4³

and 36 can also be written as 6×6 or 6²

Now, 4ˣ= 4³ and 6ʸ= 6²

We see that 4 lies on both the sides and 6 is also same on both sides .

since, in two cases bases are same so,it gets automatically cancelled.

=>4ˣ= 4³

=>x=3

=>6ʸ= 6²

=>y=2

Now,we find x = 3 and y =2

We have to find x⁴+y⁴

Now,just put the values of x and y into this:

=>(3)⁴+(2)⁴

=>3×3×3×3+2×2×2×2

=>81+16

=>97

hence,the value of x⁴+y⁴ is 97